Finance Calculator
- Updated
- Formula shown
- Free, no sign-up
Results
PMT = −$1,798.65 with N = 360, I/Y = 6%
| Year | Payments | Interest added | Balance |
|---|---|---|---|
| 1 | −$21,583.82 | $17,899.78 | $296,315.96 |
| 2 | −$21,583.82 | $17,672.56 | $292,404.71 |
| 3 | −$21,583.82 | $17,431.32 | $288,252.21 |
| 4 | −$21,583.82 | $17,175.21 | $283,843.60 |
| 5 | −$21,583.82 | $16,903.29 | $279,163.07 |
| 6 | −$21,583.82 | $16,614.61 | $274,193.86 |
| 7 | −$21,583.82 | $16,308.12 | $268,918.16 |
| 8 | −$21,583.82 | $15,982.72 | $263,317.06 |
| 9 | −$21,583.82 | $15,637.26 | $257,370.50 |
| 10 | −$21,583.82 | $15,270.49 | $251,057.17 |
Sign convention: money you receive is positive and money you pay out is negative. A loan you take out has a positive PV and negative payments; savings have a negative PV and payments and a positive FV.
How to use the finance calculator
- Pick the unknown: the number of periods (N), the annual rate (I/Y), the present value (PV), the payment (PMT) or the future value (FV).
- Enter the other four, with signs: money you receive is positive, money you pay is negative. Use 0 for anything that doesn't apply.
- Set P/Y to how many payments a year there are. N is the total number of payments, so 30 years of monthly payments is N = 360.
- Leave C/Y as "Same as payments" unless interest compounds on a different schedule, and choose END or BGN for when payments happen.
The time value of money equation
i = (1 + I/Y ÷ (100 × C/Y))C/Y ÷ P/Y − 1
i is the rate per payment period and S is 1 for payments at the beginning of each period (BGN) and 0 for the end (END). When payments and compounding happen at the same frequency, i is simply I/Y ÷ 100 ÷ P/Y. The equation says that, once every cash flow is moved to the same date with interest, the money going in and the money coming out balance exactly. PV, PMT and FV come straight from it. N uses logarithms. I/Y has no closed form, so it is found numerically, the way financial calculators and spreadsheet RATE functions do it.
The sign convention, in plain terms
Think of each amount from your own pocket. If the money comes to you, it is positive. If it leaves you, it is negative. A problem with every amount the same sign has no answer, because you can't only pay and never receive (or the reverse).
| Situation | PV | PMT | FV |
|---|---|---|---|
| Taking out a loan or mortgage | + (you get the cash) | − (you repay) | 0, or − for a balloon |
| Saving or investing | − (you deposit) | − (you keep depositing) | + (you get it back) |
| Drawing an income from a lump sum | − (you invest it) | + (you receive income) | 0, or + for what's left |
| Buying a bond | − (the price) | + (coupons) | + (face value) |
Worked examples
- Mortgage payment: N = 360, I/Y = 6, PV = 300,000, FV = 0, P/Y = 12. PMT = −$1,798.65. The minus sign means you pay it.
- Savings: N = 120, I/Y = 5, PV = −1,000, PMT = −200. FV = $32,703.47, positive because you get it back.
- Payoff time: a $5,000 balance at 18% with $200 monthly payments: PV = 5,000, PMT = −200, FV = 0. N = 31.57 months, so the last payment is a smaller one in month 32.
- Rate needed: to turn $10,000 into $20,000 in 10 years with P/Y = 1, set PV = −10,000 and FV = 20,000. I/Y = 7.177%.
- Payment timing: a $30,000 lease-style loan at 7% for 36 months with a $15,000 residual (FV = −15,000) costs $550.66 a month with END payments but $547.46 with BGN, because each payment arrives a month earlier.
- Different compounding: $100,000 over 300 months at 5% compounded semi-annually (C/Y = 2, common for Canadian mortgages) gives a payment of $581.60, against $584.59 with monthly compounding.
Common mistakes
- N in years instead of periods. With monthly payments, 5 years is N = 60.
- Missing minus sign. If you get "no solution", check that at least one amount is negative.
- Wrong P/Y. The calculator divides I/Y by P/Y. A monthly loan with P/Y = 1 is treated as yearly payments.
- Rounded payments. Solving FV with a payment rounded to the cent can leave a few cents or dollars of balance, which is real: it is the rounding.
For single-purpose versions of these problems, see the present value, future value and interest rate calculators.
Frequently asked questions
What do N, I/Y, PV, PMT and FV mean?
N is the number of payment periods, I/Y the annual interest rate, PV the present value (the amount now), PMT the regular payment and FV the future value (the amount at the end). Enter any four to solve for the fifth.
Why is my payment negative?
The calculator uses the cash-flow sign convention: money you receive is positive and money you pay is negative. For a $300,000 mortgage at 6% over 360 months, PV is +300,000 and the payment comes out as −$1,798.65 because you pay it.
Why do I get no solution?
Usually because every amount has the same sign. To solve for N or I/Y, at least one cash flow must be positive and one negative. For savings, enter PV and PMT as negative deposits and FV as a positive amount.
What is the difference between END and BGN?
END means payments happen at the end of each period, as with most loans. BGN means they happen at the start, as with rent and many leases. A $30,000 loan at 7% for 36 months with a $15,000 residual costs $550.66 a month with END payments and $547.46 with BGN.
What are P/Y and C/Y?
P/Y is payments per year and C/Y is compounding periods per year. They are usually the same. Canadian mortgages compound semi-annually with monthly payments: $100,000 over 300 months at 5% costs $581.60 a month with C/Y = 2.