Loan or mortgage-style payments
You get the money now and repay it in equal payments. Solve for the payment, loan amount, number of payments, or rate.
- Loan amount$25,000.00
- Payment$483.32
- Number of payments60
- Interest rate per year6%
- Total paid$28,999.20
How the financial calculator works
Every loan or savings plan with equal payments and compound interest fits one equation with five numbers. You enter four, and the calculator isolates the fifth.
| Key | Meaning | Example |
|---|---|---|
| N | Number of payment periods | 60 monthly payments |
| I/Y | Interest rate per year | 6% a year |
| PV | Present value | $25,000 borrowed today |
| PMT | Payment each period | $483.32 a month |
| FV | Future value | Balance or balloon at the end |
| P/Y | Payments per year | 12 for monthly |
The Loan tab is for debt: you receive the PV and make payments. The Savings tab is for saving: you put in a PV and deposits, then take out the FV. For the version with cash-flow signs, like a handheld calculator, see the HP-12C financial calculator.
Worked examples
| Solve for | Inputs | Answer |
|---|---|---|
| PMT (payment) | PV $25,000, I/Y 6%, N 60, monthly | $483.32 |
| PMT, payments at the start | PV $25,000, I/Y 6%, N 60, monthly | $480.92 |
| PMT, mortgage-style | PV $300,000, I/Y 6.5%, N 360, monthly | $1,896.20 |
| PV (loan amount) | PMT $483.32, I/Y 6%, N 60, monthly | $25,000.00 |
| FV (final balance) | PV $1,000, PMT $200, I/Y 12%, N 12, monthly | $3,663.33 |
| I/Y (rate) | PV $1,000, FV $1,210, N 2, yearly | 10% per year |
For plain compound growth without deposits, use the compound interest calculator. For interest that never compounds, see simple interest.
Payments at the end or the start of the period
With payments at the end of each period (an ordinary annuity), the first payment is due one period after the loan starts. Most loans and mortgages work this way. With payments at the start (an annuity due), the first payment is due right away, as with rent paid in advance or a lease with the first payment at signing.
Each early payment earns or costs one extra period of interest, so BGN payments come out a little smaller: $483.32 drops to $480.92, which is $483.32 ÷ 1.005.
Common mistakes
- Using a yearly rate with the wrong number of payments per year. Set P/Y to 12 for monthly payments.
- Using the quoted rate when the contract has fees. Add fees by hand, since the calculator only uses the rate you type.
- Solving for N or I/Y when the payment is too small to cover the interest. Then the balance never reaches zero and there is no solution.
- Forgetting a balloon payment: a lease or a balloon loan has an FV above zero.
Go deeper
Frequently asked questions
How do I use a financial calculator?
Pick a tab, choose what to solve for, and fill in the other values. Set P/Y to match your payments, such as 12 for monthly.
What do N, I/Y, PV, PMT, and FV mean?
N is the number of periods, I/Y the yearly interest rate, PV the present value, PMT the payment each period, and FV the future value. Any four determine the fifth.
How do I calculate a loan payment?
Use PMT = PV × i ÷ (1 − (1 + i)^−N), with i as the rate per period. For $25,000 at 6% over 60 months, i = 0.5% and the payment is $483.32.
How do I find the interest rate on a loan?
On the Loan tab, solve for I/Y with the loan amount, payment, and number of payments. $10,000 paid back in 12 payments of $888.49 works out to about 12% a year.
What is the difference between END and BGN?
END means payments at the end of each period. BGN means payments at the start, so each payment gets one more period of interest and the payment is a bit smaller.
Does this replace an HP-12C or a TI BA II Plus?
It handles the same regular cash-flow problems with N, I/Y, PV, PMT, and FV. It does not do uneven cash flows like NPV or IRR.
Sources and review
- Financial mathematics: formulas for equal payments (annuities) with compound interest.