Andrew and emma garfield invested $8,000 in a savings account paying 5% annual interest when their daughter, angela, was born. they also deposited $1,000 on each of her birthdays until she was 18 (including her 18th birthday).

$45,093

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.

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