Question

Find the monthly payment that will yield the given future value. (Round your answer to the nearest cent.)

$250,000 at
10(1/2)%
interest for forty-two years; ordinary annuity

Answer 1

To calculate the monthly payment for a $250,000 future value at 10.5% interest over 42 years, use the future value of an ordinary annuity formula. Divide $250,000 by the calculated divisor using the monthly interest rate and number of payments. Then round to the nearest cent.

Step-by-step explanation:

To find the monthly payment that will yield a future value of $250,000 at a 10(1/2)% interest rate (which is 10.5%) for forty-two years in the context of an ordinary annuity, we can use the future value of an ordinary annuity formula given by:

FV = Pmt × {((1 + r)^n - 1) / r}

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

In this problem, FV = $250,000, r = 10.5% annual interest rate divided by 12 months, and n = 42 years × 12 months/year. Plugging in these values:

$250,000 = Pmt × {((1 + 0.105/12)^(42×12) - 1) / (0.105/12)}

Solving for Pmt:

Pmt = $250,000 / {((1 + 0.105/12)^(42×12) - 1) / (0.105/12)}

Calculate the exact number for the divisor, then divide $250,000 by this number to get the monthly payment value. Finally, round your answer to the nearest cent.