# Formula for Amortizing Loan Payment

### What is an Amortizing Loan?

An amortizing loan (or amortized loan) is a type of loan that comes with periodic, scheduled payments of both the principal and interest amount. With amortized loans, borrowers need to repay the interest expense for the period. After that, they must pay an additional amount which will reduce the principal amount of the loan. There are various types of amortizing loans, such as auto loans, home loans, personal loans, etc.

Amortizing loans can be beneficial for both lenders and borrowers. For the borrower, these come with lower costs. Since the principal amount decreases with each payment, they have to pay lower interests on further installments. Similarly, with each repayment, lenders get a portion of their principal amount back. Therefore, they can reduce their credit risk through these loans.

### How to calculate Amortizing Loan payments?

Usually, amortizing loans come with amortization schedules. The schedule contains details of the payments that borrowers need to make every period. For each period, the interest payment depends on the principal amount for the last period. Therefore, the interest payments at the start of the loan will be the highest. On the other hand, interest payments during the end will be the lowest.

Similarly, the principal repayments at the start of the period will be the lowest while in the end, it will be the highest. It is because amortizing loans come with fixed payments each period for borrowers. These amortizing loan payments include a mix of both interest and principal amounts. However, for each repayment, the mix between both will be different.

As mentioned, the first payments will include a higher mix of interest payments and lower principal amounts. The final payments will consist of lower interest amounts and higher principal amounts. It is because the total repayment stays the same. Therefore, as the interest payment decreases, the principal repayments increase.

Borrowers and lenders can use the following formula for amortizing loan payments.

Amortizing Loan Payment = (PV x R) / [1 – (1 + R)^(-n)]

In the above formula, ‘PV’ represents the present value of the loan. ‘R’ denotes the per period interest rate, usually calculated by dividing the annual interest rate by the number of interest payments per year. Lastly, ‘n’ represents the number of payments in a year. Using the above formula for amortizing loan payments, lenders can calculate their total amount.

The following formula is also helpful in calculating the interest portion of the amortizing loan payment.

Interest on Amortizing Loan Payment = PV x (R / n)

In the above formula, ‘PV’ represents the present value of the loan. ‘R’ is the periodic interest rate on it. Lastly, ‘n’ represents the total number of payments.

### Example

A lender pays a \$100,000 loan to a borrower at an interest rate of 9%. The loan period is five years, and the borrower has to make monthly repayments. Therefore, they can calculate the amortizing loan payment using the following formula.

Amortizing Loan Payment = (PV x R) / [1 – (1 + R)^(-n)]

In the above formula, ‘PV’ will be the \$100,000 value of the loan. ‘R’ will be the periodic interest rate, which will be 0.75% (9%/12 payments). ‘n’ will be the number of total payments. Since the loan lasts for five years and the borrower has to make a payment every month, the total number of payments will be 60 (5 years x 12 months). Therefore, the amortizing loan payment will be.

Amortizing Loan Payment = (\$100,000 x 0.75%) / [1 – (1 + 0.75%)^(-60)]

Amortizing Loan Payment = \$2,076

### Conclusion

Amortizing loans are debt obligations where borrowers have to repay a portion of the principal amount along with periodic interest payments. Borrowers can use the amortizing loan payment formula above to calculate the repayments on their amortizing loans.

## Further questions

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