Question

Sean’s grandparents have been depositing $200 into Sean’s savings account on every month, starting from the first month after his first birthday. The account pays 6% interest compounded monthly. Immediately after Sean’s grandparents make the last monthly deposit on Sean’s 18th birthday, the amount of money in Sean’s savings account will be closest to:

a. $25,539.50
b. $70,646.22
c. $25,667.19
d. $75,003.53

Answer 1

The amount of money in Sean's savings account on his 18th birthday will be closest to $70,646.22.

Step-by-step explanation:

To calculate the amount of money in Sean's savings account after his 18th birthday, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, Sean's grandparents deposit $200 every month, so the principal amount is $200. The interest rate is 6% (or 0.06) and it is compounded monthly, so n = 12. The total number of deposits made will be 18 * 12 = 216 times. Therefore, substituting the values into the formula:

A = 200(1 + 0.06/12)^(12*18) = $70,646.22

Therefore, the amount of money in Sean's savings account on his 18th birthday will be closest to $70,646.22.