Financial Math

Homework 5

October 4, 2022

1. (Problem 15.4) Calculate the present value of 300 paid at the end of each year for 20 years using an annual effective interest rate of 8%.

2. (Problem 15.22) The accumulated value of an n year annuity-immediate is four times the present value of the same annuity. Calculate the accumulated value of 100 in 2n years (note that this is just the value of 100 at t = 2n, not an annuity of 100).

3. (Problem 15.25) To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years. The annual effective rate of interest is i. You are given (1 + i)n = 2.0. Determine i.

4. (Problem 16.1) An 8-year annuity due has a present value of $1,000. If the effective annual interest rate is 5%, then what is the value of the periodic payment?

5. (Problem 16.3) A 5-year annuity due has periodic cash flows of $100 each year. Find the accumulated value of this annuity if the effective annual interest rate is 8%.

6. (Problem 16.6) Megan wants to buy a car in 4 years for 18,000. She deposits X at the beginning of each month for four years into an account earning 6% compounded monthly. Calculate X.

7. (Problem 16.22) Jerry will make deposits of 450 at the end of each quarter for 10 years. At the end of 15 years, Jerry will use the fund to make annual payments of Y at the beginning of each year for 4 years, after which the fund is exhausted. The annual effective rate of interest is 7%. Determine Y .

8. (Problem 17.16) Simplify a15 (1 + ν15 + ν30) into one symbol.

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