TVM Calculator (Time Value of Money)

Pick the value you want to find, fill in the other four and read the answer.

Result

Future value (FV)

1,628.89

Using 5% per period, payments at the end of each period.

How to use TVM Calculator (Time Value of Money)

Choose what to solve for: future value, present value, payment, number of periods or interest rate.
Fill in the other fields. Use negative numbers for money you pay or invest and positive numbers for money you receive.
Set periods per year, for example 12 when N counts months, and whether payments fall at the start or end of each period.
Read the answer, which updates as you type.

About this tool

The time value of money is the idea that a sum today is worth more than the same sum later, because today's money can earn interest. Almost every loan, saving plan and annuity is built on five linked numbers: the number of periods (N), the interest rate, the present value (PV), the regular payment (PMT) and the future value (FV). If you know any four, the fifth is fixed.

This calculator solves for any one of them. The signs matter, as on a financial calculator: money that leaves your pocket, such as a deposit or a loan repayment, is entered as negative, and money you receive is positive. A starting deposit of -1,000 that grows to 1,628.89 is a positive future value.

Interest is applied once per period. If N is a number of months, enter 12 periods per year so the annual rate is divided correctly. Payments at the end of each period are called an ordinary annuity, and payments at the start are called an annuity due, which earns one extra period of interest on each payment.

How it is calculated

With r as the rate per period, n as the number of periods and t as 0 for end-of-period or 1 for start-of-period payments, the five values satisfy PV × (1 + r)^n + PMT × (1 + r × t) × ((1 + r)^n − 1) ÷ r + FV = 0.

FV, PV, PMT and N are rearranged directly. The interest rate has no direct formula, so the calculator finds it by narrowing down the range until the equation balances.

Worked examples

Invest 1,000 for 10 years at 5% a year with no payments: the future value is 1,628.89.
To reach 50,000 in 10 years at 6% a year with monthly payments, enter N = 120, rate = 6, periods per year = 12 and FV = 50,000. The payment is -305.10, shown negative because it is money you pay in.

Tips for better results

If the answer says no solution, check the signs. Money in and money out must have opposite signs.
Keep N and the periods per year in step. Monthly payments over 5 years is N = 60 with 12 periods per year.
Test an answer by putting it back in and solving for a different value. The result should match.

Frequently asked questions

What do N, I/Y, PV, PMT and FV mean?

N is the number of periods, I/Y is the yearly interest rate, PV is the present value, PMT is the payment each period and FV is the future value.

Why is my payment negative?

Money you pay out is negative by convention. The size of the number is what matters.

What is the difference between payments at the start and the end of a period?

A payment at the start of a period earns interest for one extra period, so the future value is a little higher and the payment needed is a little lower.

Is this the same as a financial calculator?

It uses the same standard equation, so with the same inputs and sign conventions it gives the same answers, apart from rounding.

Are my numbers saved or sent anywhere?

No. The calculation runs in your browser on your own device. Nothing you type is sent to Paul Digital or any other server.

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Privacy

The calculation runs in your browser on your own device. The numbers you type are not sent to Paul Digital or any other server. Results are estimates from the numbers you enter and are not financial, tax or legal advice.