How to use the repayment calculator
Enter the loan balance and the interest rate, then choose how the rate compounds and how often you pay. Pick Within a fixed time and enter when you want to be debt free to see the payment it takes, or pick With a fixed payment and enter what you can afford to see how long the loan lasts. Either way you get the total interest, the payoff date and a full repayment schedule.
Repayment formulas
The calculator first turns the yearly rate into the rate of one payment period: i = (1 + rate ÷ k)k ÷ f − 1, with k compounding periods and f payments a year. The payment to repay a balance P in n payments is M = P × i ÷ (1 − (1 + i)−n), and the number of payments a fixed payment M takes is n = −ln(1 − P × i ÷ M) ÷ ln(1 + i).
Repayment calculator example
- Within a fixed time: $10,000 at 10% repaid monthly over 5 years takes $212.47 a month, $2,748.23 of interest in total.
- With a fixed payment: paying $200 a month on the same loan takes 5 years and 4.9 months and costs $2,989.74 of interest. The last payment is smaller, $189.74.
Payoff time by payment
| Monthly payment | Time to repay | Total interest |
|---|---|---|
| $150 | 8 years and 1.7 months | $4,657.48 |
| $200 | 5 years and 4.9 months | $2,989.74 |
| $250 | 4 years and 0.9 months | $2,214.57 |
| $300 | 3 years and 3.2 months | $1,763.95 |
| $500 | 1 year and 10 months | $984.81 |
For $10,000 at 10% compounded monthly. The payment must be more than one month's interest, $83.33, or the balance never goes down.
How compounding changes the cost
| Compound | Effective yearly rate | Monthly payment | Total interest |
|---|---|---|---|
| Annually (APY) | 10.000% | $210.36 | $2,621.35 |
| Semi-annually | 10.250% | $211.48 | $2,688.62 |
| Monthly (APR) | 10.471% | $212.47 | $2,748.23 |
| Daily | 10.516% | $212.67 | $2,760.16 |
| Continuously | 10.517% | $212.68 | $2,760.57 |
The same 10% rate on $10,000, repaid monthly over 5 years. The more often the rate compounds, the higher the real cost: compounded daily, the loan costs $11.93 more than compounded monthly. Most U.S. loans quote an APR compounded monthly; a rate quoted as an APY is compounded yearly.
Repayment in Excel
- Payment:
=PMT(10%/12,60,-10000)returns $212.47. - Number of payments:
=NPER(10%/12,-200,10000)returns 64.95. - With daily compounding, use the rate of one month:
=PMT((1+10%/365)^(365/12)-1,60,-10000)returns $212.67.
Ways to repay faster
- Pay a little more than the required payment. Every extra dollar goes straight to the balance.
- Pay every two weeks instead of monthly: 26 half payments add up to one extra monthly payment a year.
- Put windfalls such as a tax refund or a bonus toward the loan.
- Refinance to a lower rate if your credit has improved since you took the loan.
Related calculators
For a loan with a deferred payment or a bond, use the loan calculator. The amortization calculator adds extra payments to a schedule, and the interest rate calculator finds the rate from the payment you were quoted. To repay several debts at once, use the debt payoff calculator.