Question

You're prepared to make monthly payments of $240, beginning at the end of this month, into an account that pays 9 percent interest compounded monthly. How many payments will you have made when your account balance reaches $63,000? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

To calculate the number of payments you will have made when your account balance reaches $63,000, you can use the formula for the future value of an ordinary annuity. Plugging in the given values and solving the equation, the answer is 232 payments.

Step-by-step explanation:

To calculate the number of payments you will have made when your account balance reaches $63,000, you can use the formula for the future value of an ordinary annuity:

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

In this formula, FV represents the future value, P represents the payment amount, r represents the interest rate per period, and n represents the number of periods.

Plugging in the given values, we have:

FV = $63,000, P = $240, r = 9% / 12 (monthly interest rate), and n is the number of payments.

Rearranging the formula to solve for n, we get:

n = log((FV * r / P) + 1) / log(1 + r)

Plugging in the values, we have:

n = log(($63,000 * (9% / 12) / $240) + 1) / log(1 + (9% / 12))

Calculating this expression gives us n ≈ 231.35.

Since we cannot have a fraction of a payment, we need to round the number of payments up to the nearest whole number.

Therefore, the number of payments you will have made when your account balance reaches $63,000 is 232 payments.