Enter any three of the four fields (principal, annual interest rate, number of payments, payment) and leave one blank to calculate the missing value. This calculator also displays an amortization schedule showing how the interest portion of each payment diminishes as the balance is paid down.
- Front Loaded Interest Calculator
- All Personal Finance Calculators
- Compound Interest Days Calculator
- Interest Reserve Calculator
- Compound Interest Every Minute Calculator
Diminishing Balance (Amortizing) Payment Formula
The following equation is used to calculate the fixed periodic payment for an amortizing loan where interest is charged on the outstanding (diminishing) balance.
Payment = (P × r) / [1 - (1 + r)^(-n)]
- Where Payment is the total periodic payment amount (e.g., $/month)
- P is the principal amount ($)
- r is the periodic interest rate (decimal form). For monthly payments, r = (annual rate ÷ 100) ÷ 12
- n is the total number of payments (periods)
- The interest portion in period t is: Interestt = Balancet−1 × r, where Balancet−1 is the outstanding balance before payment t
To calculate the fixed periodic payment, multiply the principal by the periodic interest rate, then divide by [1 – (1 + r)-n]. To find the diminishing interest portion of a specific payment, multiply the outstanding balance before that payment by r.
What Is Diminishing Interest (Reducing-Balance Interest)?
Definition:
Diminishing interest refers to an interest calculation method in which the interest portion of each payment is based on the outstanding principal. As the principal is paid down, the portion of each payment that goes toward interest decreases over time (assuming the loan is being amortized).
How to Calculate Diminishing Interest?
Example Problem:
The following example outlines the steps and information needed to calculate the payment on a diminishing-balance loan and illustrates how the interest portion diminishes over time.
First, determine the principal. In this example, the principal is $10,000.
Next, determine the periodic interest rate (r) and the total number of payments (n). In this example, let’s assume the monthly interest rate is 0.5% (0.005 in decimal) with 24 total payments.
Finally, calculate the payment using the formula above:
Payment = (P × r) / [1 – (1 + r)-n]
Payment = (10,000 × 0.005) / [1 – (1 + 0.005)-24]
This gives a payment of approximately $443.24 per month. The first month’s interest is $10,000 × 0.005 = $50.00, and the interest portion will be smaller in later months as the outstanding balance declines.
FAQ
How is diminishing interest different from a flat interest rate?
With a flat interest rate, the interest is calculated on the entire principal amount for the entire term of the loan. In a diminishing interest model, the interest portion is recalculated each period based on the remaining principal, which generally results in lower overall interest costs.
Can a diminishing interest model save me money?
Yes, since the interest portion decreases as the principal is repaid, you typically pay less total interest over the life of the loan compared to a flat rate model of the same rate and term.
What factors impact a diminishing interest schedule?
The primary factors include the principal amount, the interest rate, and the frequency of payments. Making larger payments or additional payments toward the principal can further reduce the amount of interest paid over time.