Homework #1 (each 4 points) 1. At his death in 1790, Benjamin Franklin left 1,000 pounds each to the cities of Boston and Philadelphia on the condition that they would not touch the money for 100 years. Boston’s bequest, which was equivalent to about $4,600, had ballooned to $332,000 by 1890. a. Determine the equivalent annual rate of return between 1790 and 1890. b. If the city of Boston had left this bequest in a fund earning 5% per year between 1890 and 1990, what would have been the value of the fund in 1990? 2. Here is a series of cash flows with an interest rate of 8% per period: End of period 1-5 6-10 Project X $1000 2000 Project Y $2,000 1,000
a. Find the equivalent present values of the two projects. b. Find the equivalent values of the two projects at the end of 10 periods. c. Find the equivalent uniform series of the two projects. 3. Assuming an (effective) interest rate of 10% per annum: a. How much must be invested today in order to provide an annuity of $20,000 per year for 4 years, with the first payment occurring exactly 10 years from now. b. How much must be invested today in order to provide an annuity of $10,000 every 6 months for 4 years (8 payments) with the first payment occurring exactly 10 years from now? c. A sum of $2,000 will be deposited into a savings account at the beginning of each year for 10 years. If the fund accrues interest at the rate of 10% per year, how much will be in the fund after 10 years? 4. How many months will it take to pay off a $525 debt, with monthly payments of $15 at the end of each month, if the interest is at the (nominal) annual rate of 18% compounded monthly? 5. You are offered the opportunity to invest $100 for 4 years with simple interest computed at the rate of 10% per year. a. How much (principal plus accrued interest) will you receive at the end of 4 years? b. What is your actual rate of return (per year) on this proposed investment? c. If you invested the $100 elsewhere at a nominal rate of 10% per...
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