Question

Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child's college education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 9%. The parents deposit $2400 on their daughter's first birthday. After 10 payments, they increase the annual amount to $4,000. Assuming that the parents have already made the deposit for their daughter's 18th birthday, then how much will be available for the daughter's college expenses on her 18th birthday?

Answer 1

FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
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
Time	10
annual depost	2400
interest	9%
FV at T10=	2400* ((((1 + 9%) ^ 10) - 1) / 9%)
FV at T10=	36,463.03
Now this amount remains invested till 18th birthday so for next 8 years
Accumulated amount at t18=	36463.0313*(1+9%)^8
Accumulated amount at t18=	72,654.87
Accumulation of depost made from t11 to t18
Time	8
annual depost	4000
interest	9%
FV at T18=	4000* ((((1 + 9%) ^ 8) - 1) / 9%)
FV at T18=	44,113.90
so total accumulation	72654.87+44113.90
so total accumulation	116,768.77