Question

Problem 04.048 Equivalence When PP < CP How much would your parents have to deposit each month into an account that grows at a rate of 6% per year compounded quarterly if they want to have $76,000 at the end of year 3 to cover part of your college expenses? Assume no interperiod compounding. Parents have to deposit $ each month.

Answer 1

Annuity formula i FUA = P / (1+r) - 1 where, FuA = Future value of Annuity = $16000 r= interest rate (.e., 6-1) per year. but interest is componded seminan guartely then the interest rate will be 1.5% (ie. 61 - 1.5.1) n = 3 years Since compounded is grantely then - the perted will be a 12 (1.0, 3 x 4 = 12). 0.015 76000 P 71.1956 - 1) 1 0.015 76000 = P (0.1956 10-015 7600D = ß 13.04 P P = 76000 13.04 P = 5828.22

Now $5828.22 is the payment of 3 months because the interest was torresponding compounding quartely the monthly payment will be & 1942.14. So the monthly paymen $ 58 23.22 = $ 1942.74 Answer: $ 1942.74 Parents have to deposit & 1942-14 each month