Cumulative Interest Paid
Cumulative Interest Paid
Total interest paid over the first p payments of an amortizing loan, summed payment by payment from the schedule. Each payment is capped at the balance plus interest, so the total stops growing once the loan is paid off.
When to use: Use to see how much of what you have paid so far went to interest rather than principal, or to compare the interest cost of two loans over the same number of payments.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| CumInterest | Cumulative Interest | Interest paid through payment p | $ |
| PV | Original Loan | Original loan amount | $ |
| PMT | Payment | Periodic payment amount | $ |
| k | Interest Rate | Annual interest rate | % |
| m | Payments per Year | Number of payments per year | integer |
| p | Payments Made | Number of payments to sum over | integer |
Real-Life Examples
Example 1: Five Years into a Mortgage
A $300,000 mortgage at 6.5% with monthly payments of $1,896.20. How much interest has been paid after 60 payments?
Given
Step-by-Step
Five years in, $94,605 of the $113,772 paid has gone to interest. Early payments on a long loan are mostly interest because the balance is still large.
Example 2: First Year of an Auto Loan
A $25,000 car loan at 7% over 5 years, $495.03 per month. Interest paid in the first 12 payments?
Given
Step-by-Step
Of the $5,940 paid in year one, $1,613 was interest. The share falls every year as the balance shrinks.
Frequently Asked Questions
Interest is charged on the outstanding balance, which is largest at the start. As payments reduce the balance, each successive payment carries less interest and more principal.
No. Once the balance reaches zero the schedule stops, so p beyond the payoff point returns an error rather than inventing interest on a loan that no longer exists.