Time Value of Money Calculator

Solve for

N — number of periods

I/Y — annual interest rate (%)

PV — present value

FV — future value

Payments per year

Payments at

PMT — payment per period

-1,199.10

Signs matter, as on a BA II Plus or in Excel: money you pay out is negative, money you receive is positive. Borrowing $200,000 is PV 200000 with a negative payment.

Balance year by year

Year	Payments	Interest	Balance
1	14,389.21	11,933.19	197,543.98
2	14,389.21	11,781.71	194,936.47
3	14,389.21	11,620.88	192,168.14
4	14,389.21	11,450.14	189,229.06
5	14,389.21	11,268.86	186,108.71
6	14,389.21	11,076.41	182,795.91
7	14,389.21	10,872.08	179,278.77
8	14,389.21	10,655.15	175,544.71
9	14,389.21	10,424.84	171,580.34
10	14,389.21	10,180.33	167,371.45
11	14,389.21	9,920.73	162,902.97
12	14,389.21	9,645.13	158,158.88
13	14,389.21	9,352.52	153,122.19
14	14,389.21	9,041.87	147,774.85
15	14,389.21	8,712.06	142,097.69
16	14,389.21	8,361.90	136,070.38
17	14,389.21	7,990.15	129,671.31
18	14,389.21	7,595.47	122,877.57
19	14,389.21	7,176.45	115,664.81
20	14,389.21	6,731.58	108,007.17
21	14,389.21	6,259.27	99,877.23
22	14,389.21	5,757.84	91,245.86
23	14,389.21	5,225.47	82,082.12
24	14,389.21	4,660.27	72,353.17
25	14,389.21	4,060.21	62,024.17
26	14,389.21	3,423.14	51,058.10
27	14,389.21	2,746.78	39,415.67
28	14,389.21	2,028.70	27,055.16
29	14,389.21	1,266.33	13,932.27
30	14,389.21	456.94	0.00

This works like the five TVM keys on a financial calculator. Pick what you want to solve for (the number of periods N, the annual rate I/Y, present value PV, the payment PMT or future value FV), type the other four, and the answer appears as you type. The signs follow the same rule as a BA II Plus or Excel's PMT and FV functions: money you pay out is negative, money you receive is positive. So a $200,000 mortgage at 6% over 30 years is N 360, I/Y 6, PV 200000, FV 0, and PMT comes back as −1,199.10. Choose how many payments a year, and whether they happen at the end of each period (an ordinary annuity, the default) or the beginning (an annuity due). Open the yearly table to see how much went to interest and what's left each year. It's handy for checking homework in a finance course, because the numbers match the calculator in your hand.

Built by Bob QA by Ben Shipped October 9, 2026

How to use

1
Under Solve for, pick the value you don't know: N, I/Y, PV, PMT or FV.
2
Type the other four. Use a minus sign for money you pay out, like a deposit or a loan payment.
3
Pick payments per year. Monthly means N counts months and the rate is split across 12 periods.
4
Choose End for an ordinary annuity or Beginning for an annuity due.
5
Read the answer, copy it, and open Balance year by year to see the schedule.

📈 Future Value Calculator 💵 Annuity Calculator 🏦 Loan Calculator 💰 Compound Interest Calculator

Frequently asked questions

Why is my answer negative?

Because of the sign rule. Every TVM problem has money moving in two directions, and the calculator needs to know which is which. Money you receive is positive and money you pay is negative. Borrow $200,000 (positive PV) and the payment comes out negative, because you pay it. Save $100 a month (negative PMT) and the future value comes out positive, because you get it back. If you get an error, a sign is usually the reason.

What's the difference between End and Beginning?

End is an ordinary annuity: each payment happens at the end of its period, like most loans. Beginning is an annuity due: each payment happens at the start, like rent or a savings deposit made on payday. Paying at the start gives every payment one more period of interest. $100 a month for 10 years at 5% grows to $15,528.23 paid at the end of each month, and $15,592.93 paid at the start.

How does it solve for the interest rate?

There's no formula that gives the rate directly, so it does what a financial calculator does: it tries rates until the five values balance, to a tiny fraction of a cent. If two rates both work (which can happen when cash flows change sign more than once), it shows the one closest to zero, which is the one textbooks use.

Why does N come out with a decimal?

Because the last payment doesn't need to be a full one. If N comes back as 104.6, it takes 105 payments, and the 105th is smaller than the others. The calculator says so under the answer.

How is the rate compounded?

Once per payment period. Monthly payments mean monthly compounding, with I/Y divided by 12. That's the default on a BA II Plus (P/Y = C/Y) and what most textbook problems assume.

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