Issuu on Google+

Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler

CHAPTER 2 EXERCISES 2.1 1-6: Recall that the maturity value is the amount to be paid to the lender at the end of the note’s term to pay off the loan. The proceeds is that amount given to the borrower/buyer for the note. The proceeds is the same things as what we would call the principal if we were looking at things as simple interest. The discount is the difference between the proceeds and the maturity value. The discount is equal to what we would call the interest if we were looking at things as simple interest. 1.

a. b. c.

$800 $750 $800 - $750 = $50

2.

a. b. c.

$20,000 $20,000 - $1,000 = $19,000 $1,000

3.

a. b. c.

$20,000 $18,000 $20,000 - $18,000 = $2,000

4.

a. b. c.

$23,467.19 $24,500 $24,500 - $23,467.19 = $1,032.81

5.

a. b. c.

$1,308.55 $1275 $1,308.55 - $1275 = $33.55

6.

a. b. c.

$25 $20 $5

7. a. b.

D = MdT D = ($10,000)(0.09)(200/365) D = $493.15 Recall that discount is subtracted from the maturity value to get the proceeds. $10,000 - $493.15 = $9,506.85

2-1


Timothy J. Biehler 8.

D = MdT D = ($1,000)(0.03)(5) D = $150 The proceeds are found by subtracting discount from the maturity value: $1,000 - $150 = $850

9.

D = MdT D = ($100,000)(0.35)(2/12) D = $5,833.33 This discount would be subtracted from the $100,000 maturity value: $100,000 - $5,833.33 = $94,166.67

10.

D = MdT D = ($20,000)(0.0319)(175/365) D = $305.89 Discount is subtracted from the maturity value to get the proceeds: $20,000 - $305.89 = $19,694.11

11.

D = MdT $250 = M(0.125)(6/12) 250 = M(0.0625) Divide both sides by 0.0625 M = $4,000.00 12.

The amount of the discount is $25,000 - $24,325 = $675. D = MdT $675 = $25,000(d)(90/365) 675 = 6164.383562d Divide both sides by 6164.383562 d = 0.1095 = 10.95% 13.

The amount of the discount is $10,000 - $9,759.16 = $240.84 D=MdT $240.84 = ($10,000)(d)(217/365) 240.84 = 5945.205479d Divide both sides by 5945.205479 d = 0.0405099539 = 4.05% 14.

The amount of the discount is $5,000 - $4,975 = $25 D = MdT $25 = $5,000(0.04)T 25 = 200T Divide both sides by 200 T = 0.125 years Multiply by 365 and round to convert to days T = 46 days

2-2


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler 15.

The amount of the discount is $800 - $785.21 = $14.79 D = MdT $14.79 = ($800)(0.75)T 14.79 = 600T Divide both sides by 600 T = 0.2465 years Multiply by 365 and round to convert to days T = 9 days 16. April 8 is day 90+8 = 98; June 17 is day 151+17 = 168. So the term of the note is 168-98 = 70 days. D = MdT D = ($2,000)(0.0572)(70/365) D = $21.94 Subtract the discount from the maturity value to find the proceeds $2,000 - $21.94 = $1,978.06 17.

The amount of the discount is $180 - $160 = $20. D = MdT $20 = ($180)d(1/12) 20 = 15 d Divide both sides by 15 d = 1.3333333333 = 133.33% 18.

$8,000 - $7,856.02 = $143.98

19.

The amount of the discount is $5,000 - $4,876.52 = $123.48 D = MdT $123.48 = $5,000(d)(182/365) 123.48 = 2493.150685 d Divide both sides by 2493.150685 d = 0.495276923 = 4.95% 20.

$23,507 - $1,851.03 = $21,655.97

21.

D = MdT D = $875,000(0.24)(45/365) D = $25,890.41 To find the proceeds, subtract the discount from the maturity value. $875,000 - $25,890.41 = $849,109.59

2-3


Timothy J. Biehler 22. June 28 is day 151+28 = 179; December 31 is day 365. The term is therefore 365 – 179 = 186. D = MdT D = ($1,000)(0.0589)(186/365) D = $30.01 23.

The amount of the discount is $875.39 - $850 = $25.39 D = MdT $25.39 = ($875.39)(d)(50/365) 25.39 = 119.9164384 d Divide both sides by 119.9164384 d = 21.17% 24. April 1 is day 90+1 = 91; November 15 is day 304+15 = 319. The term is 319 – 91 = 228 days. D = MdT D = ($10,000)(0.0821)(228/365) D = $512.84 The proceeds are $10,000 - $512.84 = $9,487.16 25.

D = MdT D = $10,000(0.0532)(28/365) D = $40.81 The proceeds are $10,000 - $40.81 = $9,959.19 26.

The amount of the discount is $1,000 - $982.56 = $17.44 D = MdT $17.44 = $1,000(d)(91/365) 17.44 = 249.3150685 d Divide both sides by 249.3150685 d = 0.0699516484 = 7.00% 27. The term of this loan is 15 – 1 = 14 days. (You could also calculate the number of days by finding the Julian dates for May 15 and May 1 and subtracting, but since the dates fall in the same month this is not really necessary to find the term.) D = MdT D = $17,500,000(0.0398)(14/365) D = $26,715.07 The proceeds are $17,500,000 - $26,715.07 = $17,473,284.93

2-4


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler 28.

a. The amount of the discount is $5,000 - $4,905.75 = $94.25 D = MdT $94.25 = ($5,000)(0.04)T 94.25 = 200T Divide both sides by 200 T = 0.47125 years Multiply by 365 and round to convert years to days T = 172 days b. March 12 is day 59+12 = 71. 172 days after that is day 71+172 = 243. This date is actually one of the numbers listed in the abbreviated table. The maturity date is August 31. 29.

The amount of the discount is $100,000 - $99,353.29 = $646.71 D = MdT $646.71 = $100,000(0.0444)T 646.71 = 4440T Divide both sides by 4440 T = 0.1456554054 years Multiply by 365 and round to convert years to days T = 53 days April 3 is day 90+3 = 93. 53 days after that is day 93+53=146. The largest number in the abbreviated table less than 146 is 120, the end of April. So the maturity date is 146-120 = 26 days after that: May 26, 2007. 30.

The amount of the discount is $150,000 - $117,300 = $32,700 D = MdT $32,700 = $150,000(d)(9/12) 32,700 = 112,500 d Divide both sides by 112,500 d = 29.07% Note that this rate is based on an assumed remaining life expectancy. Because the insured’s actual time left can not be known for certain, the actual simple discount rate cannot be known in advance.

2-5


Timothy J. Biehler EXERCISES 2.2 1-4.

Recall the definition of these terms. Both the principal (a) and proceeds (e) refer to the amount borrowed. The maturity value (b) and (f) refers to the amount to be paid by the borrower to the lender at the end of the loan’s term, whether simple interest or simple discount. The amount of interest (c) is the same as the amount of discount (g). The face value (d) when using simple interest is the same as the principal. When using simple discount, the face value (h) is the same as the maturity value. 1.

a) $875 b) $900 c) $900 - $875 = $25 d) $875 (same as (a)) e) same as a) f) same as b) g) same as c) h) same as b)

2.

a) $4,753,259 b) $5,000,000 c) $5,000,000 - $4,753,259 = $246,741 d) same as a) e) same as a) f) same as b) g) same as c) h) same as b)

3.

a) $352.45 b) $363.79 c) $363.79 - $352.45 = $11.34 d) same as a) e) same as a) f) same as b) g) same as c) h) same as b)

4.

a) $18,355.17 b) $18,759.15 c) $18,759.15 - $18,355.17 = $403.98 d) same as a) e) same as a) f) same as b) g) same as c) h) same as b)

2-6


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler 5. The amount of interest is $10,000 - $9,393.93 = $606.07. This is also the amount of discount. a) I = PRT $606.07 = $9,393.93(R)(300/365) 606.07 = 7721.038356 R R = 7.85% b) D = MdT $606.07 = $10,000(d)(300/365) 606.07 = 8219.178082 d d = 7.37% 6. a)

b)

7. a)

b)

8. a)

b)

The amount of interest/amount of discount is $70,000 - $62,500 = $7,500. I = PRT $7,500 = $62,500(R)(9/12) 7,500 = 46,875 R R = 16.00% D = MdT $7,500 = $70,000(d)(9/12) 7,500 = 52,500 d d = 14.29% The amount of interest/amount of discount is $20 - $15 = $5. I = PRT $5 = $15(R)(14/365) 5 = 0.5753424658 R R = 869.05% D = MdT $5 = $20(d)(14/365) 5 = 0.767123877 d d = 651.79% The amount of interest/amount of discount is $725,000 - $576,300 = $148,700 I = PRT $148,700 = $576,300(R)(2) 148,700 = 1,152,600 R R = 12.90% D = MdT $148,700 = $725,000(d)(2) 148,700 = 1,450,000 d d = 10.26%

2-7


Timothy J. Biehler 9.

D = MdT D = ($7,500)(0.12)(1) D = $900 The proceeds are $7,500 - $900 = $6,600 I = PRT $900 = ($6,600)R(1) 900 = 6,600R R = 13.64% 10.

D = MdT D = ($5,000)(0.0835)(150/365) D = $171.58 The proceeds are $5,000 - $171.58 = $4,828.42 I = PRT $171.58 = ($4,828.42)R(150/365) 171.58 = 1,984.282192 R R = 8.65% 11.

D = MdT D = ($4,250)(0.0955)(37/365) D = $41.14 The proceeds are $4,250 - $41.14 = $4,208.86 I = PRT $41.14 = ($4,208.86)(R)(37/365) 41.14 = 426.6515616 R R = 9.64% 12.

D = MdT D = ($10,000)(0.0548)(73/365) D = $109.60 The proceeds are $10,000 - $109.60 = $9,890.40 I = PRT $109.60 = $9,890.40(R)(73/365) 109.60 = 1978 R R = 5.54% 13.

D = MdT D = ($120,000)(0.40)(1) D = $48,000 The proceeds are $120,000 - $48,000 = $72,000 I = PRT $48,000 = ($72,000)(R)(1) 48,000 = 72,000(R) R = 66.67%

2-8


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler 14.

a) (1.5%)($1,043.59) = (0.015)($1,043.59) = $15.65 b) $1,043.59 - $15.65 = $1,027.94 c) D = MdT $15.65 = ($1,043.59)(d)(7/365) 15.65 = 21.01405479 d d = 78.20% d) I = PRT $15.65 = ($1,027.94)(R)(7/365) 15.65 = 19.71391781 R R = 79.39%

15.

a) b)

c)

(0.0175)($789.95)+$5=$18.82 D = MdT $18.82 = ($789.95)d(10/365) 18.82 = 21.64246575 d d = 86.96% The proceeds (=principal) is $789.95 - $18.82 = $771.13 I = PRT $18.82 = ($771.13)(R)(10/365) 18.82 = 21.12684932 R R = 89.08%

16. The amount of the discount is (0.04)($3,279.46) = $131.18 Discount rate: D = MdT $131.18 = ($3,279.46)d(30/365) 131.18 = 269.5446575d d = 48.67% Interest rate: The proceeds (= principal) is $3,279.46 - $131.18 = $3,148.28 I = PRT $131.18 = ($3,148.28)(R)(30/365) 131.18 = 258.7627397 R R = 50.70% 17. The amount of the discount is (0.01)($750,000) = $7,500 Discount rate: D = MdT $7,500 = ($750,000)d(16/365) 7,500 = 32,876.71233 d d = 22.81% Interest rate: The proceeds (= principal) is $750,000 - $7,500 = $742,500. I = PRT $7,500 = ($742,500)R(16/365) 7,500 = 32,547.94521 R R = 23.04%

2-9


Timothy J. Biehler 18. The amount of interest/discount is $475,000 - $471,500 = $3,500. Discount rate: D = MdT $3,500 = ($475,000)(d)(27/365) 3,500 = 35,136.9863 d d = 9.96% Interest rate: I = PRT $3,500 = $471,500(R)(27/365) 3,500 = 34,878.08219 R R = 10.03% 19.

The amount of the discount is: D = MdT D = ($10,000)(0.0444)(135/365) D = $164.22 The proceeds were $10,000 - $164.22 = $9,835.78 I = PRT $164.22 = ($9,835.78)R(135/365) 164.22 = 3,637.891233 R R = 4.51% 20.

a) $482.36 b) $500 c) $500 - $482.36 = $17.64 d) same as a) e) same as a) f) same as b) g) same as c) h) same as b)

21. The discount is (0.10)($79.95) = $8.00. The amount paid would be $79.95 $8.00 = $71.95. I = PRT $8.00 = $71.95(R)(3/12) 8 = 17.9875 R R = 44.48% 22.

D = MdT D = ($25,000)(0.0509)(18/365) D = $62.75 The proceeds would have been $25,000 - $62.75 = $24,937.25 I = PRT $62.75 = ($24,937.25)(R)(18/365) 62.75 = 1,229.782192 R R = 5.10%

2-10


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler 23.

D = MdT D = ($1,800,000)(0.095)(3/12) D = $42,750 So the company would receive proceeds of $1,800,000 - $42,750 = $1,757,250 To compare the two offers, we need to know the equivalent simple interest rate, to be able to compare it to the other offer’s simple interest rate. I = PRT $42,750 = ($1,757,250)(R)(3/12) 42,750 = 439,312.5 R R = 9.73% Even though 9.63% sounds like a higher rate compared to 9.5%, in actuality 9.63% is a better deal since the 9.5% discount rate is equivalent to a 9.73% interest rate. 24.

$1,295 - $1,249.35 = $45.65

25. The amount of discount/amount of interest is $45.65. We can now calculate the simple discount rate. I = PRT $45.65 = $1249.35(R)(45/365) 45.65 = 154.0294521 R R = 29.64% This is actually higher than the rate charged by the credit card. 26.

I = PRT I = ($14,357)(0.15)(100/365) I = $590.01 The maturity value is $14,357 + $590.01 = $14,947.01 D = MdT $590.01 = ($14,947.01)d(100/365) 590.01 = 4,095.071233 d d = 14.41% 27. The simple interest rate should always be higher than the simple discount rate, because the principal is always less than the maturity value. 7/31/07 must be the misprint. 28.

D = MdT D = ($1,000)(0.25)(2) D = $500 The proceeds are $1,000 - $500 = $500 I = PRT $500 = ($500)R(2) 500 = 1000R R = 50%

2-11


Timothy J. Biehler 29.

D = MdT D = ($1,000)(0.18)(5) D = $900 The proceeds are $1,000 - $900 = $100 I = PRT $900 = ($100)R(5) 900 = 5000R R = 180% 30.

a)

D = MdT D = ($10,000)(0.06)(1/12) D = $50 The proceeds are $10,000 - $50 = $9,950 I = PRT $50 = ($9,950)(R)(1/12) 50 = 829.1666667 R R = 6.03% b) Done the same way as a) but with T=3/12 c) Done the same was as a) but with T = 6/12/07 d) Done the same way as a) but with T = 1 e) The point of these comparisons is that there is no one simple interest rate that is equivalent to a given discount rate. The equivalent simple interest rate for a given situation depends not only on the discount rate, but also on the term

2-12


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler EXERCISES 2.3 1. a)

I = PRT I = ($3,000)(0.0845)(125/365) I = $86.82 The maturity value is $3,000 + $86.82 = $3,086.82 b) The note was sold 45 days after it started. Since the original term was 125 days, this means that 125 – 45 = 80 days were left. D = MdT D = ($3,086.82)(0.0768)(80/365) D = $51.96 The proceeds are $3,086.82 - $51.96 = $3,034.86 2.

a) I = PRT I = $5,255(0.1225)(200/365) I = $352.73 The maturity value is $5,225 + $352.73 = $5,607.73 b) The note was sold 80 days after it started. Since the original term was 200 days, this means that 200 – 80 = 120 days were left. D = MdT D = $5,607.73(0.0928)(120/365) D = $171.09 The proceeds are $5,607.73 - $171.09 = $5,436.64 3.

I = PRT I = ($2,750)(0.16)(100/365) I = $120.55 The maturity value is $2,750 + $120.55 = $2,870.55 The problem states that the note was sold when 30 days were left until maturity. D = MdT D = ($2,870.55)(0.12)(30/365) D = $28.31 The proceeds are $2,870.55 - $28.31 = $2,842.24 4.

I = PRT I = $8,000(0.103)(220/365) I = $496.66 The maturity value is $8,000 + $496.66 = $8,496.66 The note was sold 90 days after it started. Since the original term was 220 days, this means that 220 – 90 = 130 days were left. D = MdT D = ($8,496.66)(0.114)(130/365) D = $344.99 The proceeds are $8,496.66 - $344.99 = $8,151.67

2-13


Timothy J. Biehler

5. January 16 is day 16; March 25 is day 59+25 = 84; November 15 is day 304 + 15 = 319. (We are assuming this is not a leap year.) The note’s original term was 319 – 16 = 303 days. I = PRT I = ($10,000)(0.0992)(303/365) I = $823.50 The maturity value is $10,000 + $823.50 = $10,823.50 When the note was sold, the remaining term was 319 – 84 = 235 days. D = MdT D = $10,823.50(0.0825)(235/365) D = $574.91 The proceeds are $10,823.50 - $574.91 = $10,248.59 6. February 11 is day 31+11 = 42; February 26 is day 31+26 = 57; July 5 is day 181+5 = 186. The note’s original term was 186 – 42 = 144 days. I = PRT I = ($2,500)(0.1502)(144/365) I = $148.14 The maturity value was $2,500 + $148.14 = $2,648.14 When the note was sold, the remaining term was 186 – 57 = 129 days. D = MdT D = ($2,648.14)(0.0931)(129/365) D = $87.13 The proceeds are $2,648.14 - $87.13 = $2,561.01 7.

October 18 is day 273 + 18 = 291; November 23 is day 304+23 = 327. I = PRT I = ($6,000)(0.0675)(200/365) I = $221.92 The maturity value is $6,000 + $221.92 = $6,221.92. The time between when Neela made the loan and when she sold the note was 327 – 291 = 36 days. That means there were 200 – 36 = 164 days left when it was sold. D = MdT D = ($6,221.92)(0.1281)(164/365) D = $358.12 The proceeds are $6,221.92 - $358.12 = $5,863.80.

2-14


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler 8. 289.

April 30 is day 120; February 7 is day 31+7 = 38; October 16 is day 273+16 =

The note extends across part of 2006 and part of 2007. The note’s life in 2006 is 365 – 120 = 245 days. The note’s life in 2007 is 38 days. In total, the note’s term is 283 days. I = PRT I = ($538,000)(0.0459)(283/365) I = $19,146.46 The maturity value is $538,000 + $19,146.46 = $557,146.46 When the note was sold, it still had 365 – 289 = 76 days to run in 2006 and 38 days in 2007, for a total remaining term of 114 days. D = MdT D = ($557,146.46)(0.06)(114/365) D = $10,440.77 The proceeds are $557,146.46 - $10,440.77 = $546,705.69 9.

a) Look at things from Troupsburgs’ perspective: $3,034.86 $3,086.82 |------------------------------------------| 80 days The amount of interest is $3,086.82 - $3,034.86 = $51.96 I = PRT $51.96 = ($3,034.86)(R)(80/365) 51.96 = 665.1747945 R R = 7.81% b) Look at things from Jasper’s perspective: $3,000 $3,034.86 |------------------------------------------| 45 days I = PRT $34.86 = $3,000(R)(45/365) 34.86 = 369.8630137 R R = 9.43% c) The fact that the note was sold does not affect Colline in any way. She signed up to pay 8.45%, she pays 8.45%.

2-15


Timothy J. Biehler 10.

a) Look at things from Ron’s perspective: $5,255 $5,436.64 |------------------------------------------| 80 days The interest earned was $181.64 I = PRT $181.64 = ($5,255)(R)(80/365) 181.64 = 1151.780822 R R = 15.77% b) Harry is not affected by the fact the note is sold. He agreed to pay 12.25%, he pays 12.25% c) Look at things from Hermione’s perspective $5,436.64 $5,607.73 |-----------------------------------------| 120 days The interest earned was $5,607.73 - $5,436.64 = $171.09 I = PRT $171.09 = ($5,436.64)(R)(120/365) 171.09 = 1787.388493 R R = 9.57% 11.

a) Look at things from Shawn’s point of view. $2,842.24 $2,870.55 |--------------------------------------------------| 30 days I = PRT $28.31 = ($2,842.24)(R)(30/365) 28.31 = 233.6087671 R R = 12.12% b) Look at things from Thierry’s perspective $2,750 $2,842.24 |----------------------------------------------------| 70 days I = PRT $92.24 = ($2,750)(R)(70/365) 92.24 = 527.3972603 R R = 17.49% c) Audra is not affected by the fact that her note is sold. 16%

2-16


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler 12.

a) The borrower is not affected by the note being sold. 10.3% b) From Allegany Federal Credit Union’s point of view $8,000 $8,151.67 |---------------------------------------------------| 90 days I = PRT $151.67 = ($8,000)(R)(90/365) 151.67 = 1,972.60274 R R = 7.69% c) From Limestone Capital’s point of view $8,151.67 $8,496.66 |---------------------------------------------------| 130 days I = PRT $344.99 = ($8,151.67)R(130/365) 344.99 = 2,903.334521 R R = 11.88%

13.

a) The borrower is not affected by the sale. 9.92% b) From the original lender’s point of view $10,000 $10,248.59 |---------------------------------------------------| 68 days I = PRT $248.59 = ($10,000)(R)(68/365) 248.59 = 1863.013699 R R = 13.34% c) From the secondary buyer’s point of view. $10,248.59 $10,823.50 |---------------------------------------------------| 235 days I = PRT $574.91 = $10,248.59 (R)(235/365) 574.91 = 6,598.40726 R R = 8.71%

2-17


Timothy J. Biehler 14.

a) From Kevin’s point of view: $2,500 $2,561.01 |-----------------------------------------------------| 15 days I = PRT $61.01 = $2,500(R)(15/365) 61.01 = 102.739726 R R = 59.38% b) From Byron’s point of view $2,561.01 $2,648.14 |-----------------------------------------------------| 129 days I = PRT $87.13 = $2,561.01(R)(129/365) 87.13 = 905.1240822R R = 9.63% c) Tien is not affected by the fact that her note was sold. 15.02%

15.

a) From Neela’s point of view: $6,000 $5,863.80 |-----------------------------------------------------| 36 days I = PRT -$136.20 = ($6,000)(R)(36/365) -136.20 = 591.7808219 R R = -23.02% b) From Vic’s point of view $5,863.80 $6,221.92 |-----------------------------------------------------| 164 days I = PRT $358.12 = ($5,863.80)(R)(164/365) 358.12 = 2,634.693699 R R = 13.59% c) Davis is not affected by his note being sold. 6.75%

2-18


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler 16.

a) The hospital is not affected by the note being sold. 4.59% b) From Macedon Funding’s point of view $538,000 $546,705.69 |-----------------------------------------------------| 169 days I = PRT $8,705.69 = ($538,000)(R)(169/365) 8,705.69 = 249,101.3699 R R = 3.49% c) From Palnyra’s point of view $546,705.69 $557,146.46 |----------------------------------------------------| 114 days I = PRT $10,440.77 = $546,705.69(R)(114/365) 10,440.77 = 170,751.9141 R R = 6.11%

17.

Maturity Value = P + PRT $13,576.25 = P + P(0.0675)(75/365) 13,576.25 = P + P(0.013869863) 13,576.25 = (1.013869863)P P = $13,390.53

18.

Maturity Value = P + PRT $7,645.14 = P + P(0.0936)(20/365) 7,645.14 = P + P(0.0051287671) 7,645.14 = P(1.0051287671) P = $7,606.13

19.

I = PRT I = ($5000)(0.075)(60/365) I = $61.64 The maturity value is $5000+$61.64 = $5,061.64 Maturity Value = P + PRT $5,061.64 = P + P(0.08)(15/365) 5,061.64 = P + P(0.0032876712) 5,061.64 = (1.0032876712)P P = $5,045.05 20.

Maturity Value = P + PRT $10,000 = P + P(0.0521)(38/365) 10,000 = P + P(0.0054241096) 10,000 = (1.0054241096)P P = $9,946.05

2-19


Timothy J. Biehler 21.

I = PRT I = ($2,000)(0.0937)(100/365) I = $51.34 The maturity value is $2,000 + $51.34 = $2,051.34 D = MdT D = $2,051.34(0.0895)(70/365) D = $35.21 The proceeds are $2,051.34 - $35.21 = $2,061.13 22.

I = PRT I = ($547,813)(0.0644)(60/365) I = $5,799.31 The maturity value is $547,813 + $5,799.31 = $553,612.31 D = MdT D = $553,612.31(0.0675)(35/365) D = $3,583.31 The proceeds are $553,612.31 - $3,583.31 = $550,029.00 From Alephone’s point of view $547,813 $550,029 |--------------------------------------------------| 25 days I = PRT $2,216 = ($547,813)(R)(25/365) 2,216 = 37,521.43836 R R = 5.91% 23. May 8 is day 120+8 = 128; October 15 is day 273+15 = 288; July 17 is day 181+17 = 198. The term of the note is 288 – 128 = 160 days. I = PRT I = ($800)(0.055)(160/365) I = $19.29 The maturity value is $800 + $19.29 = $819.29. The note had 288 – 198 = 90 days left when it was sold. D = MdT D = $819.29(0.0388)(90/365) D = $7.84 The proceeds of the sale of the note are $819.29 - $7.84 = $811.45 From Andy’s point of view: $800 $811.45 |----------------------------------------------------------| 70 days

2-20


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler I = PRT $11.45 = $800(R)(70/365) 11.45 = 153.4246575 R R = 7.46% From Curt’s point of view: $811.45 $819.29 |----------------------------------------------------------| 90 days I = PRT $7.84 = ($811.45)(R)(90/365) 7.84 = 299.0835616 R R = 3.92% 24.

I = PRT I = $29,375(0.0825)(180/365) I = $1,195.12 The maturity value of the note is $29,375 + $1,195.12 = $30,570.12 D=MdT D = ($30,570.12)(0.07125)(150/365) D = $895.12 The proceeds are $30,570.12 - $895.12 = $29,675.00 From Emerson’s point of view $29,375 $29,675 |-------------------------------------------------| 30 days I = PRT $300 = ($29,375)(R)(30/365) 300 = 2,414.383562 R R = 12.43% 25.

a) I = PRT I = ($35,000)(0.075)(120/365) I = $863.01 The maturity value of the note is $35,000 = $863.01 = $35,863.01 b) D = MdT D = ($35,863.01)(0.052)(30/365) D = $153.28 The proceeds are $35,863.01 - $153.28 = $35,709.73 c) From the bank’s point of view $35,000 $35,709.73 |------------------------------------------------------| 90 days I = PRT

2-21


Timothy J. Biehler

d)

26. 170.

$709.73 = ($35,000)(R)(90/365) 709.73 = 8,639.136986 R R = 8.22% From the private investor’s point of view $35,709.73 $35,863.01 |----------------------------------------------------| 30 days I = PRT $153.28 = ($35,709.73)(R)(30/365) 153.28 = 2,935.046301 R R = 5.22% May 6 is day 120+6 = 126; July 7 is day 181+7 = 188; June 19 is day 151+19 =

This is a discount note to begin with. When Ronda bought it it had 188 – 126 = 62 days left. D = MdT D = ($10,000)(0.0653)(62/365) D = $110.92 So Ronda bought the note for $10,000 - $110.92 = $9,889.08. Ronda’s point of view. She held the note for 170 – 126 = 44 days. From her point of view: $9,889.08 $9,984.50 |---------------------------------------------------| 44 days I = PRT $95.42 = ($9,889.08)(R)(44/365) 95.42 = 1,192.108274 R R = 8.00% 27.

Chico is not affected by the sale. 13.29%

28.

April 1 is day 90+1 = 91; May 12 is day 120+12 = 132. I = PRT I = ($40,000)(0.1163)(100/365) I = $1,274.52 The maturity value is $40,000 + $1,274.52 = $41,274.52 The original lender held the note for 132 – 91 = 41 days. So when it was sold it had 100 – 41 = 59 days left. D = MdT D = ($41,274.52)(0.2439)(59/365) D = $1,627.25 The proceeds were $41,274.52 - $1,627.25 = $39,647.27

2-22


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler From the lender’s point of view: $40,000 $39,647.27 |------------------------------------------------------------| 41 days I = PRT -$352.73 = ($40,000)(R)(41/365) -352.73 = 4,493.150685 R R = -7.85% 29.

I = PRT I = ($2,500,000)(0.0325)(3) I = $243,750 The maturity value is $2,500,000 + $243,750 = $2,743,750 D = MdT D = ($2,743,750)(0.0433)(2) D = $237,608.75 The proceeds are $2,743,750 - $237,608.75 = $2,506,141.25 From Localville’s point of view: $2,500,000 $2,506,141.25 |-------------------------------------------------------------| 1 year The amount of interest is $2,506,141.25 - $2,500,000 = $6,141.25 The simple interest rate is I = PRT $6,141.25 = ($2,500,000)(R)(1) 6,141.25 = 2,500,000R R = 0.25% 30.

The borrower is not affected by the sale of the note.

31.

Sean was the borrower, he is not affected by the sale of the note.

32. Even though both the simple interest rate and the simple discount rate are 5%, the simple discount rate is applied to the maturity value, so it means that when the note was sold, the amount of discount taken would be more than the amount of interest earned at 5%. Therefore, the interest rate earned must be less than 5%. If you still have doubts about this, try it for yourself, making up the details of the amount borrowed and the times involved.

2-23


Timothy J. Biehler 33.

Calculate the amount he paid: $9,856.22 Calculate the amount he sold the note for: $9,949.55 $9,856.22 $9,949.55 |------------------------------------------------------------| 93 days I = PRT $93.33 = $9,856.22(R)(93/365) R = 3.72% 34.

Calculate the maturity value: $26,061.64 D = MdT $260.64 = $26,061.64(0.08)T T = 46 days were left when the note was sold. So the note was sold 109 days after July 5. July 5 is day 181+5 = 186, so the note was sold on day 186+109 = 295. Converting from Julian to regular date we get October 22.

2-24


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler CHAPTER TWO EXERCISES 1. D = MdT D = ($18,340)(0.113)(90/365) D = $511.01 The maturity value is $18,340 - $511.01 = $17,828.99 2. a) February 28 is day 31+28 = 59; December 15 is day 334+15 = 349. The note’s term is 349 – 59 = 290 days. D = MdT D = ($25,000)(0.14)(290/365) D = $2,780.82 The maturity value is $25,000 - $2,780.82 = $22,219.18. b) I = PRT $2,780.82 = $22,219.18(R)(290/365) 2780.82 = 17,653.59507(R) R = 15.75% 3.

I = PRT I = ($12,700)(0.052)(200/365) I = $361.86 The maturity value is $12,700 + $361.86 = $13,061.86 D = MdT D = ($13,061.86)(0.0475)(170/365) D = $288.97 The proceeds are $13,061.86 - $288.97 = $12,772.89 4.

D = MdT $285 = ($10,000)(0.0509)(T) 285 = 509T T = 0.5599214145 years Multiply by 365 to convert years to days: T = 204 days 5. September 25 is day 243+25 = 268; March 30 is day 59+30 = 89. The note lives for 365 – 268 = 97 days in 2006 and 89 days in 2007, so the total term is 97+89 = 186 days. D = MdT D = ($20,000)(0.0627)(186/365) D = $639.02 The proceeds are $20,000 - $639.02 = $19,360.98 I = PRT $639.02 = ($19,360.98)(R)(186/365) 639.02 = 9,866.143233 R R = 6.48%

2-25


Timothy J. Biehler 6.

D = MdT $200 = M(0.08)(6/12) 200 = M(0.04) M = $5,000

7.

Discount: D = MdT $20 = $700(d)(2/12) 20 = 116.6666667 d D = 17.14% Interest: I = PRT $20 = $680(R)(2/12) 20 = 113.3333333 R R = 17.65%

8.

Interest: I = PRT $511 = ($11,346)(R)(180/365) 511 = 5595.287671 R R = 9.13% Discount: D = MdT $511 = ($11,857)(d)(180/365) 511 = 5847.287671 d d = 8.74%

9.

I = PRT I = ($23,000)(0.093)(150/365) I = $879.04 The maturity value is $23,000 + $879.04 = $23,879.04 D = MdT D = ($23,879.04)(0.0826)(90/365) D = $486.35 The proceeds are $23,879.04 - $486.35 = $23,392.69 10.

a) I = PRT I = ($20,000)(0.115)(215/365) I = $1,354.79 The maturity value is $20,000 + $1,354.79 = $21,354.79 D = MdT D = ($21,354.79)(0.118)(125/365) D = $862.97 The proceeds are $21,354.79 - $862.97 = $20,491.82

2-26


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler b)

c)

I = PRT $491.82 = $20,000(R)(90/365) 491.82 = 4931.506849 R R = 9.97% Larry is unaffected by the sale. 11.5%

11.

D =MdT $7015.83 = $100,000(0.0873)(T) 7015.83 = 8730T T = 0.8036460481 years Multiply by 365 to convert to days T = 293 days 12. a)

June 5 is day 151+5 = 156. January 14 is day 14. D = MdT D = ($10,000)(0.042)(1) D = $420 The proceeds of the sale are $10,000 - $420 = $9,580. b) When he sold the note, it had 156 – 14 = 142 days left (all in 1999) D = MdT D = ($10,000)(0.041)(142/365) D = $159.51 The proceeds of the sale are $10,000 - $159.51 = $9.840.49 c) Dudley held the note for 365 – 156 = 209 days in 1998, plus 14 in 1999, for a total of 223 days. I = PRT $260.49 = ($9580)(R)(223/365) 260.49 = 5852.986301 R R = 4.45% 13.

D = MdT D = ($13,575)(0.08)(100/365) D = $297.53 The proceeds are $13,277.47. 14.

$4000 - $3750 = $250

15.

D = MdT $35.19 = ($1435.19)(d)(10/365) 35.19 = 39.32027397 d d = 89.50% I = PRT $35.19 = $1400(R)(10/365) 35.19 = 38.35616438 R R = 91.75%

2-27


Timothy J. Biehler

16.

I = PRT I = ($8,912.35)(0.085)(125/365) I = $259.43 The maturity value is $8,912.35 + $259.43 = $9,171.78 17. April 17 is day 90+17 = 107. The note matures 100 days later on day 107+100 = 207. The end of June is day 181, so the note matures 207 – 181 = 26 days later, on July 26. I = PRT 31.58 = P(0.0785)(100/365) 31.58 = (0.0215068493)P P = $1468.37 The maturity value is $1468.37 + $31.58 = $1,499.95. 18.

$5000 - $4848.59 = $151.41

19.

The borrower is unaffected by the sale of the note. 7%.

20. a) April 1 is day 90+1 = 91. The note can run for 365 – 91 = 274 days in 1999, leaving 300 – 274 = 26 days to run into 2000. That takes the maturity date to January 26, 2000. The fact that 2000 is a leap year is irrelevant since we did not cross the leap day. b) I = PRT I = ($20,000)(0.1275)(300/365) I = $2095.89 The maturity value is $20,000 + $2,095.89 = $22,059.89. 21.

$3,000 - $2,857.16 = $142.84

22.

Recall that bankers rule means that we assume 360 days per year. D = MdT D = ($3,000)(0.06)(45/360) D = $37.50 The proceeds are $5000 - $37.50 = $4,962.50 23. April 1 is day 90+1 = 91. July 8 is day 181+8 = 189. I = PRT I = ($15,000)(0.0875)(200/365) I = $719.18 The maturity value of the note is $15,000 + $719.18 = $15,719.18 The lender held the note for 189 – 91 = 98 days. That leaves 200 – 98 = 102 days to go when it was sold.

2-28


Full file at http://testbank360.eu/solution-manual-the-mathematics-of-money1st-edition-biehler D = MdT D = ($15,719.18)(0.0797)(102/365) D = $350.10 The proceeds were $15,719.18 - $350.10 = $15,369.08 24.

Interest: I = PRT $1,999.89 = ($17,357.19)(R)(250/365) 1999.89 = 11,888.4863 R R = 16.82% Discount: D = MdT $1,999.89 = ($19,357.08)(d)(250/365) 1999.89 = 13,258.27397 d d = 15.08%

25.

D = MdT D = ($10,000)(0.0501)(130/365) D = $178.44 The proceeds are $10,000 - $178.44 = $9,821.56 26.

$20,000 - $1,575 = $18,425

27.

I = PRT I = ($3,000)(0.11)(200/365) I = $180.82 The maturity value is $3,000 + $180.82 = $3,180.82. D = MdT D = $3,180.82(0.15)(170/365) D = $222.22 The proceeds of the sale are $3,180.82 - $222.22 = $2,958.60 28.

Virginia is unaffected by the sale of the note. 8.43%

29. Recall the definitions of these terms, and that the amount of interest is equal to the amount of discount. 30.

D = MdT D = ($50,000)(0.0444)(100/365) D = $608.22 The proceeds are $50,000 - $608.22 = $49,391.78

2-29


Timothy J. Biehler 31.

D = MdT $100.57 = $10,000(0.0657)(T) 100.57 = 657T T = 0.1530745814 years To convert to days multiply by 365 T = 56 days 32.

I = PRT $100.57 = ($9,899.43)(R)(56/365) 100.57 = 1518.816658 R R = 6.62%

33. April 30 is day 90+30 = 120; March 17 is day 59+17 = 76. The term is 120 – 76 = 44 days Discount: D = MdT $24.15 = ($824.15)(d)(44/365) 24.15 = 99.34958904 d d = 24.31% Interest I = PRT $24.15 = $800(R)(44/365) 24.15 = 96.43835616 R R = 25.04% 34.

The fee is (1%)($1,845.17) = (0.01)($1845.17) = $18.45. He would receive $1,845.17 - $18.45 = $1,826.72 I = PRT $18.45 = ($1,826.72)(R)(9/365) 18.45 = 45.04241096 R R = 40.96%

35.

Secondary sale: D = MdT $1055 = $10,850(d)(250/365) 1055 = 7431.506849 d d = 14.20% Interest on original lender I = PRT -$205 = ($10,000)(R)(50/365) -205 = 1369.863014 R R = 14.97%

2-30


Solution manual the mathematics of money 1st edition biehler