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University of Illinois at Urbana-Champaign Department of Industrial and Enterprise Systems Engineering IE 430 Engineering Economy (Fall 2016) Homework 4 1. Convert the given interest rates in the first column into the nominal rates listed in the second column. (Assume 4 weeks/month.) Given Interest Rate 1% per month 3% per quarter 2% per quarter 0.28% per week 6.1% per 6 months Desired Interest Rate Nominal rate per year Nominal rate per 6 months Nominal rate per year Nominal rate per quarter Nominal rate per 2 years Answer 2. A loan company offers money at 1.8% per month, compounded monthly. (a) What is the nominal interest rate? (b) What is the effective annual interest rate? (c) How many years will it take an investment to triple if interest is compounded monthly? (d) How many years will it take an investment to triple if the nominal rate is compounded continuously? 3. Suppose that $2,000 is placed in a bank account at the end of each quarter over the next 15 years. What is the future worth at the end of 15 years when the interest rate is 6% compounded (a) Quarterly? (b) Monthly? (c) Continuously? 4. You are buying a home for $350,000. (a) If you make a down payment of $100,000 and take out a mortgage on the rest of the money at 9% compounded monthly, what will be your monthly payment to retire the mortgage in 15 years? (b) Consider the seventh payment. How much will the interest and principle payments be? 5. A man is planning to retire in 15 years. Money can be deposited at 8% compounded quarterly. What quarterly deposit must be made at the end of each quarter until he retires so that he can make a withdrawal of $25,000 semiannually over the first five years of his retirement? Assume that his first withdrawal occurs at the end of six months after his retirement. 1 6. Tesla Motors manufactures high-performance battery electric vehicles. An engineer is on a Tesla committee to evaluate bids for new-generation coordinate-measuring machinery to be directly linked to the automated manufacturing of high-precision vehicle components. Three bids include the interest rates that vendors will charge on unpaid balances. To get a clear understanding of fi nance costs, Tesla management asked the engineer to determine the effective semiannual and annual interest rates for each bid. The bids are as follows: Bid 1: 9% per year, compounded quarterly Bid 2: 3% per quarter, compounded quarterly Bid 3: 8.8% per year, compounded monthly (a) Determine the effective rate for each bid on the basis of semiannual periods. (b) What are the effective annual rates? These are to be a part of the final bid selection. (c) Which bid has the lowest effective annual rate? 2