Loan & Mortgage Payment
Choose Loan / Mortgage, enter the amount you borrow as PV, the annual rate as I/YR, and the term in payment periods as N. If the balance is paid off at the end, set FV to 0 and solve for PMT. The scenario button sets PV positive, which is the cash you receive. Under Advanced options you can set payments per year (P/Y), compounding periods per year (C/Y), beginning or end of period, and whether the rate is a nominal APR or an effective annual rate. The result is principal and interest. It does not add property tax, insurance, or PMI. The mortgage payment guide uses this same setup for a worked payment, then compares rates, discount points, and a refinance break-even.
Amortization Schedule
Select Show amortization schedule under the result. Each row lists the period, payment, interest, principal, and remaining balance for the inputs currently on the page. Loans of 60 periods or fewer show every period. Longer loans are sampled: a 360-period mortgage is shown yearly, not as 360 separate lines. There is no extra-payment box. To model a larger payment, increase PMT or shorten N and open the schedule again. The amortization guide explains how to read those columns and how a higher payment shifts interest into principal.
Savings & Investment Growth
Choose Savings / Investing to start from a deposit. PV is negative because that money leaves you, and a repeating contribution goes in PMT. Leave PMT at 0 for a lump sum with no additions, then solve for FV, the contribution, the rate, or the number of periods. P/Y, C/Y, beginning versus end timing, and nominal APR versus effective annual rate work the same way as in loan mode. The calculator does not adjust for inflation and does not compare dollar-cost averaging on its own. You can solve a lump sum and a monthly contribution as two separate cases, or type a real rate instead of a nominal one. The investment growth guide shows both comparisons.
Frequently Asked Questions
What is the time value of money?▼
The time value of money (TVM) is the principle that money available today is worth more than the same amount in the future because it can earn interest. TVM calculations let you compare cash flows at different points in time by converting between present value and future value using an interest rate.
How does this compare to an HP 12C or HP 10BII calculator?▼
This calculator implements the same five-variable TVM model (N, I/YR, PV, PMT, FV) used by HP financial calculators. You can solve for any one variable given the other four, just like pressing CPT on an HP 10BII or solving on an HP 12C. It also supports compounding and payment frequency settings, and beginning/end of period payment timing.
What do the negative signs on PV and PMT mean?▼
Financial calculators follow a sign convention: money you pay out (invest, deposit, or pay on a loan) is negative, and money you receive (withdrawals, loan proceeds) is positive. For a savings scenario, you enter PV as negative (you invest it) and FV as positive (you receive it). For a loan, PV is positive (you receive the loan) and PMT is negative (you pay it back).
What is the difference between beginning-of-period and end-of-period payments?▼
End-of-period (ordinary annuity) means the payment happens after interest accrues for that period — this is the default for most loans and mortgages. Beginning-of-period (annuity due) means the payment happens first, before interest — common for rent payments and some lease structures. Beginning-of-period payments earn one extra period of interest compared to end-of-period.
What is the difference between P/Y and C/Y?▼
P/Y (payments per year) is how many times you make a payment each year — 12 for monthly, 4 for quarterly. C/Y (compounding periods per year) is how many times interest compounds per year. They are often the same, but can differ — for example, some Canadian mortgages have monthly payments (P/Y=12) but semi-annual compounding (C/Y=2).
Can I solve for the interest rate?▼
Yes. Unlike simple formulas, solving for the interest rate requires numerical methods because the TVM equation cannot be rearranged algebraically for i. This calculator uses a bisection method to find the rate — the same approach used internally by HP financial calculators.
Is my data private?▼
Calculator inputs and results stay in your browser and are not sent to our servers. There is no account and no sign-up. Google AdSense may set advertising cookies to show and measure ads. See the Privacy Policy for how advertising cookies work.
What formulas does this calculator use?▼
The core TVM equation is: PV(1+i)^N + PMT × [((1+i)^N - 1)/i] × (1+i×BEG) + FV = 0, where i is the interest rate per period, N is the number of periods, and BEG is 1 for annuity due or 0 for ordinary annuity. Solving for i requires numerical root-finding. Solving for N uses logarithms when PMT=0, or numerical methods otherwise.
Why is my interest rate result showing 'No solution'?▼
Solving for interest rate can fail if the inputs are contradictory — for example, if PV and FV have the same sign and PMT is zero, there is no interest rate that connects them. Make sure your sign convention is correct: cash out is negative, cash in is positive. Also verify that at least one cash flow has a different sign from the others.
Can I use this for mortgage calculations?▼
Yes. For a mortgage, enter the loan amount as a positive PV (you receive the money), the monthly payment as a negative PMT (you pay it), set FV to 0 (or the balloon amount), enter the annual interest rate, set P/Y=12 and C/Y=12 for monthly payments, and solve for the variable you need.