Answer:
$45,093
Step-by-step explanation:
A fix Payment for a specified period of time is called annuity. The Compounding of these payment on a specified rate is known as Future value of annuity. In this question $1,000 per year payment for 18 years at 5% interest rate is also an annuity.
We can calculate the amount of saving by calculating the future value of the given annuity.
Formula for Future value of annuity is as follow
Future value of annuity = FV = P x ( [ 1 + r ]^n - 1 ) / r
Where
P = Annual payment = $1,000
r = rate of return = 6%
n = number of years = 18 years
As given there is also an Initial Deposit at the beginning.
So, Formula will be
Future value of annuity = [ Initial deposit ( 1 + r )^n ] + [P x ( [ 1 + r ]^n - 1 ) / r ]
Future value of annuity = [ $8,000 (1 + 5%) ^18 ] + [ $1,000 ( [ 1 + 5% ]^17 - 1 ) / 5%]
Future value of annuity = $19,253 + 25,840 = $45,093
As on the 18th payment no compounding interest income is accrued yet because grandparent made it now.