Question

Starting three months after her grandson Robin's birth, Mrs. Devine made deposits of $115 into a trust fund every three months until Robin was twenty-one years old. The trust funds provides for equal withdrawals at the end of each quarter for four years, beginning three months after the last deposit. If interest is 4.62% compounded quarterly, how much will Robin receive every three months?

Robin will receive $ _____ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

Quarterly Payment	115
Annual Payment	460
Interest	4.62%
Effective annual rae	=(1+4.62%/4)^4)-1)
	4.701%
First calculate the corpus amount in 21 years
FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Corpus amount	=PMT x ((((1 + r) ^ n) - 1) / i)
Corpus amount	=460* ((((1 + 4.701%) ^ 21) - 1) / 4.62%)
	16,168
Now this will be distributed over a period of 4 years
PV of those withdrawls should be equal to corpus
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Corpus amount	=PMT x (((1-(1 + r) ^- n)) / i)
16,168	=PMT * (((1-(1 + 4.701%) ^- 4)) / 4.62%)
16,168	=PMT * 3.633
Annual withdrawl	=16168/3.633
Annual withdrawl	4450.3165
Quarterly withdrawl	=4450/4
Quarterly withdrawl	1,113