UGBA 103 Quiz #1: Individual Decision Making There are SEVEN questions in this quiz. Please complete all parts. For your reference, the present value of a T period annuity, with a per period discount rate of r and payments equal to C, that are growing at rate g is " T # 1+g C 1− PV = . r−g 1+r
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1. You are considering purchasing a new truck that will cost you $34,000. The dealer offers you 1.9% APR financing for 48 months (with payments made at the end of the month). Assuming you finance the entire $34,000 and finance through the dealer, what will your monthly payments be? Solution: First we need the monthly interest rate = APR/k = .019/12 = .001583 or .1583%. Using the annuity formula: 34000 = P M T × 1 1 ) × (1 − (1.001583) ( 0.001583 48 ).So PMT = $736.15 2. The interest on James Taggart’s credit card balances are compounded daily at an effective annual rate of 14.91%. What is the APR on his credit card? R 365 Solution: You are told that (1 + 0.01491) = 1 + AP . Thus, the APR 365 1 on his credit card is ((1 + 0.1491) 365 − 1) × 365 = 0.139006 3. Suppose you deposit $500 in an account at the end of each of the next five years. If the account earns 4% annually, how much will be in the account at the end of ten years? The present value is PV
=
500 1 1− 0.04 1.045
At the end of 10 years, this is worth: P V (1.04)10 . Thus, PV = 2225.91 and FV = 3294.89 4. Food For Less (FFL), a grocery store, is considering offering one hour photo developing in their store. The firm expects that sales from the new one hour machine will be $150,000 per year. FFL currently offers overnight film processing with annual sales of $100,000. While many of the one hour photo sales will be to new customers, FFL estimates that 60% of their current overnight photo customers will switch and use the one hour service. (a) What is the level of incremental sales associated with introducing the new one hour photo service?