Final answer:
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.