Enter the loan amount, annual interest rate, and either the number of monthly payments or the monthly payment into the calculator to see how the interest portion of each payment typically decreases over time on an amortizing loan.
Decreasing Interest Formula
The following equation is used to calculate the interest portion for a given payment on a standard amortizing loan (which is why the interest portion typically decreases over time as the balance declines).
Int_t = B_{t-1} \times \frac{r}{m}- Where Intt is the interest portion of payment t ($)
- Bt−1 is the outstanding loan balance immediately before payment t ($)
- r is the annual interest rate (decimal)
- m is the number of payments per year (for monthly payments, m = 12)
To calculate the interest portion for a specific payment period, multiply the outstanding balance at the start of that period by the periodic interest rate (for monthly payments, the periodic rate is typically r/12). Over time, as the balance is paid down, the interest portion of each installment decreases.
What is a Decreasing Interest?
Definition:
A Decreasing Interest Calculator allows users to determine how interest payments shrink over time as a loan’s principal is incrementally paid off. By inputting key data such as the loan amount, repayment schedule, and interest rate, the calculator illustrates how each payment reduces the outstanding balance and consequently lowers the interest portion in each subsequent installment.
How to Calculate Decreasing Interest?
Example Problem:
The following example outlines the steps and information needed to calculate the Decreasing Interest.
First, determine the starting balance. In this example, the loan amount is $10,000.
Next, determine the annual interest rate. In this case, the rate is 6% (or 0.06).
Then, determine the number of payments per year. Assume there are 12 monthly payments (m = 12).
Finally, calculate the interest portion for the first period using the formula above:
Int1 = (B0 × r) / m
Int1 = ($10,000 × 0.06) / 12
Int1 = $600 / 12
Int1 = $50 (first month). In later months, replace $10,000 with the remaining balance after payments; for example, if the balance were $9,000, the interest for that month would be $45.
FAQ
Does the interest portion remain the same for every payment?
No, not on a typical amortizing loan with a fixed interest rate and level payments. As a portion of each payment goes toward reducing the principal, the outstanding balance decreases. Since interest is calculated on the remaining balance, the interest portion usually shrinks with each subsequent payment.
What factors determine how quickly the interest decreases?
The primary factors include the loan amount, the interest rate, and how aggressively the principal is paid down (which depends on the payment amount and term). All else equal, a larger principal or higher interest rate means more interest early in the schedule, and larger or more frequent payments reduce the balance faster.
How can I reduce the overall interest paid on a loan?
Making extra payments toward the principal, choosing loans with favorable interest rates, and maintaining a strong credit score can help reduce the total amount of interest paid. Additionally, selecting shorter loan terms often results in faster principal reduction and less overall interest.