When you use an installment loan, you’ll repay the amount you’ve borrowed (the principal) over a set amount of time (the repayment term). You’ll also have to pay interest and fees, both of which make up the loan’s annual percentage rate (APR). The principal, loan term and APR are the three main components of your monthly payment. And by knowing each, you’ll be able to calculate how much your installments will be using a loan calculator or a mathematical formula. We’ll explain the math below, but you can also use our Simple Loan Calculator to get an idea of your monthly payment. Depending on the type of personal loan you choose, you can use three formulas to determine the monthly payment. Before you can use a formula, you’ll need to know the loan type and the variables mentioned above. They’ll be represented by the following: Monthly Loan Payment Formula
- P: The loan’s principal or the total amount of money you’ve borrowed
- r: The loan’s APR or the annual rate (the APR spread over 12 months)
- n: The number of payments you’ll make over a specific time frame
Interest-Only Loans
An interest-only loan uses a period at the beginning of the term when the borrower only pays interest. After the interest-only period ends, the borrower will pay the principal in installments or as a single lump sum.
Interest-only personal loans are rare, but if you end up using this option, you can calculate the monthly interest payment with this formula:
Monthly Payment = (P × r) ∕ n
Again, “P” represents your principal amount, and “r” is your APR. However, “n” in this equation is the number of payments you’ll make over a year.
Now for an example. Let’s say you get an interest-only personal loan for $10,000 with an APR of 3.5% and a 60-month repayment term. You can use the following steps to calculate your interest-only monthly payment:
- Multiply the principal by the APR. Take $10,000 and multiply it by your APR, 3.5%. You should get $350 as your annual interest amount.
- Divide your annual interest by the number of payments. Divide $350 by the number of payments you’ll make in a year. For this scenario, you’ll make 12 payments. You should get $29.17 as your interest-only monthly payment.
Amortizing Loans
Unlike an interest-only loan, an amortizing loan payment goes toward both the interest and principal amount. That means you’ll be paying off the loan in equal monthly installments over the repayment term.
The formula for calculating the monthly payment on an amortizing personal loan is:
Monthly Payment = P ((r (1+r)n) ∕ ((1+r)n−1))
Let’s use the previous example, but this time, the personal loan you get is amortizing. The principal (P) is $10,000, the APR is 3.5% and you have a 60-month repayment term (n). With this formula, “r” stands for the annual rate, not the APR. You can use these steps to find the monthly payment:
- Divide your APR by 12 months to get your annual interest rate (r). Divide 0.035 by 12 to get 0.002917.
- Fill out the formula. You can now plug your loan information into the above equation. You should have $10,000((0.002917(1+0.002917)60) ∕ ((1+0.002917)60−1)).
- Solve the equations inside the first set of parentheses. You should end up with $10,000((0.002917 × 1.00291760) ∕ (1.00291760−1).
- Solve the exponentials. Calculate 1.00291760 to get 1.190967. The formula is now $10,000((0.002917 × 1.190967) ∕ (1.190967−1)).
- Solve the equations in the second set of parentheses. First, multiply 0.002917 by 1.190967 to get 0.003474. Then you can subtract 1 from 1.190967 to get 0.190967 for the other half of the equation. Your formula should look like $10,000(0.003474 ∕ 0.190967).
- Divide the numbers in the final set of parentheses. Take 0.003474 divided by 0.190967 to get 0.018192.
- Multiply the loan principal by the total. You will then multiply $10,000 by 0.018192 to get your monthly payment, $181.92.
At this point, you can also use a loan calculator to make an amortization schedule for your loan. This extra step can help you visualize how your loan will be repaid over the length of the term.
