SOLUTION: At the time of his son's birth, a man invests a certain sum of money at 8%, compounded quarterly, to provide quarterly payments of 60000 each for four years, the first payment to b

Algebra.Com
Question 778287: At the time of his son's birth, a man invests a certain sum of money at 8%, compounded quarterly, to provide quarterly payments of 60000 each for four years, the first payment to be made on his son's 20th birthday. how much does the father invest?
Answer by fcabanski(1391)   (Show Source): You can put this solution on YOUR website!
The problem has two parts: 1. Determine how much is needed at the beginning of the payout period to accommodate the payouts. 2. Determine what the present value of that amount is 20 years before the payouts begin.


1. Determine the principal needed to accommodate the payouts. The formula is


i is the quarterly interest rate. Which is the rate divided by 4. .08/4 = .02.


P is the payout amount. $60,000


n is the number of payout periods. 16 - quarterly payments (4 per year) for 4 years.


A is the amount needed at the start of the annuity pay out period.



2. What is the amount he has to save now, so that it accumulates to that $830,955.81? PV = FV/(1+r)^n where r is the quarterly interest rate (.02), n is the number of quarters (20 years times 4 quarters per year = 80 quarters), and FV is the future value needed to support the annuity. That FV is 830,955.81.


PV = 830955.81/(1.02)^80 = $170,437.12

RELATED QUESTIONS

A young man is the beneficiary of a trust fund established for him 16 yr ago at his... (answered by Earlsdon)
In how many years time will a sum of money quintuple at a rate of 4% per annum compounded (answered by Theo)
How much should a couple invest at the time their son is born to provide him with $50,000 (answered by stanbon)
Jessie is the beneficiary of a trust fund established for him 21 years ago at his birth.... (answered by ikleyn)
A man invests $10,000 in an account that pays 8.5% interest per year, Compounded... (answered by ewatrrr)
Anthony invested a sum of money 6 yr ago in a savings account that has since paid... (answered by lwsshak3)
How many years, correct to the nearest tenth of a year, will it take for a sum of money... (answered by stanbon)
2. At the time of her grandson's birth, a grandmother deposits $ 1000 in an account that... (answered by ankor@dixie-net.com)
A mother invests $3000 in a bank account at the time of her daughter's birth. The... (answered by jojo14344)