Question

You would like to borrow $300,000.00 to finance a home. You wish to make monthly payments for 15 years. If the annual interest rate (APR) is quoted at 5.3%. What will the monthly payments be?

Answer 1

The equation to find the monthly payment for an installment loan is called the Equal Monthly Installment (EMI) formula. It is defined by the equation Monthly Payment = P (r(1+r)^n)/((1+r)^n-1).

• r: Interest rate. This is the monthly interest rate associated with the loan. The annual interest rate (APR or annual percentage rate) is 5.3%. To get the monthly interest rate that we need, simply divide the annual interest rate by 12.
  • 5.3% annual interest rate would be divided by 12 to get a monthly interest rate of 0.44167%. This would then be expressed as a decimal for the equation by dividing it by 100 as follows: 0.44167/100=0.0044167, which will be the monthly interest rate used in these calculations.
• n: Number of Payments. This is the total number of payments made over the life of the loan. In a 15 year loan paid monthly n = 15 x 12 = 180
• P: Principal. The amount of the loan is called the principal. In this case it is $300,000

Putting all this information in the equation:

Monthly Payment = P (r(1+r)ⁿ)/((1+r)^n-1) = 300,000 (0.053(1+0.0044167)¹⁸⁰/1+0.0044167)^180-1

Monthly Payment = $2419.53