If a borrower takes a $250,000 loan at 10% interest for 20 years, what is the monthly payment?

To determine the monthly payment on a loan using the formula for a fixed-rate mortgage, one must use the loan’s principal, interest rate, and the loan term. The loan payment formula derived from the amortization formula is:

[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} ]

Where:

• ( M ) = total monthly mortgage payment

• ( P ) = loan principal (amount borrowed)

• ( r ) = monthly interest rate (annual interest rate divided by 12)

• ( n ) = number of payments (loan term in months)

In this instance:

• The principal ( P ) is $250,000.

• The annual interest rate is 10%, so the monthly interest rate ( r ) is 10% divided by 12, which equals approximately 0.00833 (or 0.10/12).

• The loan term is 20 years, which converts to ( n = 20 \times 12 = 240 ) months.

Plugging these values into the formula gives:

[ M = 250,000 \frac{0.00833(1 + 0.00833