Question

Since your first​ birthday, your grandparents have been depositing $ 1 comma 000 into a savings account on every one of your birthdays. The account pays 6​% interest annually. Immediately after your grandparents make the deposit on your 18th​ birthday, the amount of money in your savings account will be closest​ to:

Answer 1

The amount of money in my savings account will be closest​ to $29,213

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 6% 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

Placing Value in the formula

As on the 18th payment no compounding interest income is accrued yet because grandparent made it now.

Future value of annuity = FV = $1,000 + 1,000 x ( [ 1 + 6% ]^18-1 - 1 ) / 6%

Future value of annuity = FV = $1,000 + 1,000 x ( [ 1 + 0.06 ]^17 - 1 ) / 0.06

Future value of annuity = FV = $29,213