Question

You’re prepared to make monthly payments of $225, beginning at the end of this month, into an account that pays an APR of 6.5 percent compounded monthly.

How many payments will you have made when your account balance reaches $15,000?

Answer 1

To reach a balance of $15,000 with monthly payments of $225 at an APR of 6.5 percent compounded monthly, you will need to make 93 payments.

Step-by-step explanation:

To determine the number of payments needed to reach a balance of $15,000, we can use the formula for the future value of an annuity:

`FV = P * [(1 + r)^n - 1] / r`

Where FV is the future value, P is the payment amount, r is the interest rate per period, and n is the number of periods. In this case, P = $225, r = 6.5% or 0.065, and FV = $15,000.

Plugging in these values, we can solve for n:

`15,000 = $225 * [(1 + 0.065)^n - 1] / 0.065`

By solving this equation, we find that approximately n = 92.7.

Since n represents the number of payments, we must round up to the nearest whole number, giving us a total of 93 payments.