Question

Phillip deposited $7,775 into a savings account 14 years ago. The account has an interest rate of 4.5% and the balance is currently $14,398.87. How often does the interest compound? (2 points)

daily

monthly

quarterly

annually

Answer 1

annually

Explanation:

Compound interest formula:

A = P(1 + r/n)^(nt)

amount of interest = balance - principal

Try daily:

A = 7775(1 + 0.045/365)^(365 * 14)

A = 14,597.88

This is too much money, so it was compounded less than daily.

Try monthly:

A = 7775(1 + 0.045/12)^(12 * 14)

A = 14,581.23

This is too much money, so it was compounded less than monthly.

Try quarterly:

A = 7775(1 + 0.045/4)^(4 * 14)

A = 14,547.16

This is too much money, so it was compounded less than quarterly.

Try annually:

A = 7775(1 + 0.045/1)^(1 * 14)

A = 14,398.87

This is the correct amount, so it was compounded annually.

Answer: annually