Question

Since your first birthday, your grandparents have been depositing $100 into a savings account on every one of your birthdays. The account pays 9% 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?

A) 64,362
B) 75,089
C) 53,635
D) 32181

Answer 1

To calculate the amount of money in the savings account on your 18th birthday, we can use the formula for compound interest. The amount of money will be closest to $75,089.

Step-by-step explanation:

To calculate the amount of money in the savings account on your 18th birthday, we can use the formula for compound interest. Since your grandparents have been depositing $100 every year, we need to calculate the future value of these payments with 9% interest compounded annually for 17 years (from your 1st to 18th birthday).

Using the formula:

Future Value = P(1 + r/n)^(nt)

Where P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = 100, r = 9%, n = 1 (compounded annually), and t = 17. Plugging in these values, we get:

Future Value = 100(1 + 0.09/1)^(1*17) = $75,089

Therefore, the amount of money in your savings account on your 18th birthday will be closest to $75,089.