Question

When you were born, your dear old Aunt Minnie promised to deposit $1,000 into a savings account, bearing a 5% effective annual rate, on each birthday, beginning with your first. You have just turned 22 and want the dough. However, it turns out that dear old (forgetful) aunt Minnie made no deposits on your fifth and eleventh birthdays. How much is in the account right now?

Answer 1

Answer: $34,502.85

Explanation:

The constant deposits are considered annuities.

The value at the end of 22 years is the future value of the annuity.

Future value of annuity = Annuity * ( (1 + rate)^number of years - 1 ) / rate

= 1,000 * ( ( 1 + 5%) ²² - 1) / 5%

= $38,505.21

Then subtract the future values of the deposits that your grandmother missed.

For the fifth birthday, the future value term will be 22 - 5 = 17 years

For the eleventh, the future value term will be 22 - 11 = 11 years

The amount in the account is:

= 38,505.21 - (1,000 * 1.05¹⁷) + (1,000 * 1.05¹¹)

= $34,502.85