How to use it
- Choose the kind, a loan or savings, and whether the payments are made at the end or the start of each period.
- Choose the figure to calculate in What to calculate. Its box is hidden.
- Fill in the other boxes: the yearly rate as a percentage, the number of payments and the amounts.
- Read the result, then open the balance period by period to see how each payment splits into interest and balance.
How the five figures are linked
Five figures are tied together by one equation: the present value grown over the term, plus the payments grown in the same way, gives the balance at the end. The payments of a loan reduce the balance, so they count against it; the deposits of savings add to it.
With a rate i for each payment period, n payments and a payment R in each period, the balance at the end is FV = PV (1 + i)^n ± R × ((1 + i)^n − 1) ÷ i, and for an annuity due the last term is multiplied by (1 + i). The sign is minus for a loan and plus for savings.
FV = PV × (1 + i)^n ± R × ((1 + i)^n − 1) ÷ i
PV present value (the loan amount, or the savings now)
FV balance at the end
R payment in each period
i interest rate per payment period
n number of payments
± minus for a loan, plus for savings; for an annuity due the R term is multiplied by (1 + i)Solving for each figure
- Payment: a loan repaid to zero gives the familiar R = PV ÷ a, where a = (1 − (1 + i)^−n) ÷ i is the present value factor of an annuity, as Wikipedia's Annuity page gives it.
- Present value: PV = (FV ∓ R × S) ÷ (1 + i)^n, where S is the factor of the payments; for a loan repaid to zero, PV = R × a.
- Interest rate: there is no direct formula, so the calculator scans the rates from 0% upward and narrows the root by bisection.
- Number of payments: n = ln(G) ÷ ln(1 + i), with G = (FV + K) ÷ (PV + K) and K = ± R × T ÷ i, where T is 1 for payments at the end of a period and 1 + i at the start.
What this calculator does not include
- Fees, insurance and taxes on the loan or the savings.
- Changes of the rate during the term: run the calculator again with the new rate and the balance you reached.
- Payments that change in size, and extra or early payments.
Worked example: a loan of 200,000 at 6% a year over 30 years
The rate of 6% a year, paid monthly, is 0.5% a month, and there are 360 monthly payments. Solving for the payment gives 1,199.10 a month.
The 360 payments add up to 431,676.38, so the interest is 231,676.38. In the first month the interest is 1,000.00 and the balance falls to 199,800.90.
| Figure | Value |
|---|---|
| Payment per month | 1,199.10 |
| Total of 360 payments | 431,676.38 |
| Total interest | 231,676.38 |
| Balance after month 1 | 199,800.90 |
Frequently asked questions
What is the difference between an ordinary annuity and an annuity due?
In an ordinary annuity each payment is made at the end of its period, after that period's interest. In an annuity due it is made at the start, so it earns one more period of interest. Rent is usually paid in advance, while mortgage repayments are ordinary annuities.
Why is a loan payment the same every month?
A level payment is the amount that brings the loan to zero after the last payment. Early payments are mostly interest and later ones mostly repay the balance, which the schedule shows row by row.
Can I find the interest rate instead of the payment?
Yes. There is no direct formula for the rate, so the calculator searches rates from 0% upward for the one that brings the balance out right. If no rate from 0% gives those amounts, it says so.
Does the number of payments have to be a whole number?
No. The calculator can show a fraction, such as 4.25 payments, to tell you how long the money lasts. For a real loan, use the whole number of payments the lender gives you.
Does the calculator include fees and taxes?
No. It uses only the rate and the amounts you enter. Fees, insurance and taxes increase the real cost of a loan, and the loan comparison tool adds them.
Are the figures I enter sent to a server?
No. The calculation runs in your browser, and nothing you enter is sent to us.
Sources
Figures and text last checked on Tuesday, November 10, 2026.