Question

You’re prepared to make monthly payments of $250, beginning at the end of this month, into an account that pays 8 percent interest compounded monthly. How many payments will you have made when your account balance reaches $50,000? (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, we can use the formula for the future value of an ordinary annuity. By plugging in the given values, we find that approximately 212.36 payments will have been made when the account balance reaches $50,000.

Step-by-step explanation:

To solve this problem, we can use the formula for the future value of an ordinary annuity:

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

Where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of payments.

In this case, P = $250, r = 0.08/12, and we need to find n when FV = $50,000.

Plugging in the values, we have:

$50,000 = $250 * ((1+0.08/12)^n - 1) / (0.08/12)

Solving for n:

((1+0.08/12)^n - 1) = ($50,000 * 0.08/12) / $250

((1+0.08/12)^n - 1) = 0.0267

(1+0.08/12)^n = 1.0267

n * log(1+0.08/12) = log(1.0267)

n = log(1.0267) / log(1+0.08/12)

n ≈ 212.36

Therefore, you will have made approximately 212.36 payments when your account balance reaches $50,000.