How to Calculate the Layman's Rate of Payment

Rate of payment may be an intimidating formula, but its actually pretty simple.

A rate of payment is an amount due in a specific period of time, such as each week, month or year. The formula for the rate of payment is (i*A)/[1-(1+i)^-n). While this formula looks confusing, it is rather simple to break it into layman's terms by going step by step. In order to start the calculation, you need to know the variables' original loan amount, A, the interest rate per period, i, and the number of payments, n. This formula is particularly useful for people trying to figure out how much money they can borrow and still afford the monthly payment.

Instructions

1. Determine the interest rate and time on the loan by contacting several banks to shop for the best interest rates. Often an interest rate will vary from bank to bank, so it is best to shop for the lowest interest rate. Determine how much of a loan you need. For this example, a borrower needs a $20,000 loan. The lowest interest rate he finds is 12 percent and he must make payments for the next five years. Payments are due monthly.

2. Divide the interest rate per year by the number of payments in a year. In our example, there are 12 payments in a year, so 12 percent divided by 12 payments equals 1 percent, which is the same as 0.01.

3. Determine the total number of payments by multiplying the years of repayment by the number of payments due per year. In our example, 5 years times 12 months equals 60 payments.

4. Multiply the interest rate per period by the original loan amount. Label this Part A. In our example, 0.01 times $20,000 equals $200.

5. Add 1 to the interest rate per month. Then raise the sum to the power of the negative number of payments. Raising a number to the power of is the formal way of saying use exponents. In the example, the exponent would be -60. In our example, 1 plus 0.01 equals 1.01, then 1.01 raised to the power of -60 equals 0.550449616.

6. Subtract the number calculated in Step 5 from 1. Label this Part B. In our example, 1 minus 0.550449616 equals 0.449550384.

7. Divide Part A by Part B. In our example, $200 divided by 0.449550384 equals $444.89. This is the payment rate of the loan. Each month the borrower must pay at least $444.89.

References

• The Free Dictionary: Rate of Payment
• Oak Road Systems: Loan or Investment Formulas