How to Calculate Personal Loan Payments

What Information You Need for the Calculation

To estimate your monthly payment on a fixed-rate personal loan, you need three input values: the amount you borrow (the principal), the annual interest rate, and the number of months you will take to repay it. If you already have a loan offer, all three are listed on the Truth in Lending disclosure you receive from the lender.

Lenders calculate the monthly payment using an amortization formula that keeps the payment constant while gradually shifting the split between interest and principal over time.

Be aware that the annual interest rate on your offer is different from the APR. APR includes certain fees in addition to the interest rate, so it is a more complete measure of borrowing cost, but the payment formula itself uses the nominal interest rate.

• Principal (P): The amount you borrow or the outstanding balance.
• Annual interest rate: Often shown as the "interest rate" on loan documents.
• Loan term: The number of months or years in which you agree to repay the loan.
• APR: The cost of credit expressed as a yearly rate, including finance charges and fees. APR is not the rate you plug into the amortization formula.

Sources: Consumer Financial Protection Bureau, Bankrate, Investopedia

The Amortization Formula for Fixed-Rate Loans

For a standard fixed-rate amortizing loan, lenders use this formula to calculate the monthly payment (M): M = P × [r(1 + r)^n] / [(1 + r)^n – 1].

In the formula, P is the principal amount, r is the monthly interest rate (the annual rate divided by 12), and n is the total number of monthly payments (the loan term in years times 12).

• This formula assumes level monthly payments and that interest accrues monthly, which is why the annual rate is divided by 12.
• Each monthly payment first covers the interest that has accrued, and the remainder reduces the principal. Over time, the interest portion decreases and the principal portion increases.

Sources: Bankrate, TransUnion, Investopedia

Step-by-Step Calculation Example

1. Convert the annual rate to a monthly rate: r = 0.06 / 12 = 0.005.
2. Find the total number of payments: n = 3 × 12 = 36.
3. Plug the values into the formula: M = 10000 × [0.005(1 + 0.005)^36] / [(1 + 0.005)^36 – 1].
4. First calculate (1 + 0.005)^36 = (1.005)^36 ≈ 1.1966805.
5. Then compute the numerator: 0.005 × 1.1966805 ≈ 0.0059834.
6. The full numerator becomes 10000 × 0.0059834 ≈ 59.834.
7. Now compute the denominator: 1.1966805 – 1 = 0.1966805.
8. Divide: 59.834 / 0.1966805 ≈ 304.22.

Sources: Bankrate, Investopedia

Calculating Total Interest Over the Loan Life

Once you know the monthly payment, you can find the total interest you’ll pay over the life of the loan. Multiply the monthly payment by the total number of payments, then subtract the principal amount you borrowed.

For the example above: total interest = (304.22 × 36) – 10000 ≈ 951.92, though small rounding differences may occur.

This total interest number is useful when comparing loan offers, but keep in mind that a longer term means more total interest even if the monthly payment is smaller.

Sources: TransUnion, Armed Forces Bank

How Changing the Term or APR Affects Payments

Your monthly payment and the total interest you pay are tied directly to the interest rate and the loan term. A lower rate reduces the monthly payment and total interest. A shorter term increases the monthly payment but reduces the total interest over the life of the loan.

These examples assume a fixed interest rate. For a variable-rate loan, the payment can change when the rate changes, so any calculation is only valid for the current rate period.

• A longer term means lower monthly payments but higher total interest.
• A shorter term means higher monthly payments but lower total interest.
• APR, not just the nominal rate, should be used to compare the total cost of different offers, because it includes fees.

Sources: Citi, TransUnion, Armed Forces Bank, Discover