Finance Calculator
A finance calculator solves time value of money problems, the math behind savings plans and loans. A balance grows at an interest rate over a number of periods while a regular payment adds to it or takes from it. Choose what to solve for, future value, present value, payment, number of periods or the rate, and enter the rest.
Solve for
The balance starts at the present value. At the end of each period it earns the annual rate divided by the periods per year, and then the payment is added. Enter a negative payment for money taken out, such as a loan payment or a withdrawal.
Future value
$50,969.84
Total of payments
$24,000.00
Total interest
$16,969.84
$10,000.00 present value + $24,000.00 in payments + $16,969.84 interest = $50,969.84 future value.
120 periods at 12 per year cover 10 years.
How to use the Finance Calculator
- Under Solve for, choose Future value, Present value, Payment, Periods or Rate (I/Y). The field for that value disappears and the calculator works it out from the others.
- Enter the present value, which is the balance at the start. Use 0 if you start with nothing.
- Enter the payment per period. A positive payment is added to the balance, like a monthly deposit. A negative payment is taken out, like a loan payment or a withdrawal. Use 0 if there is none.
- Enter the number of periods, the annual rate in percent and the periods per year. Monthly payments over 10 years are 120 periods at 12 per year.
- Unless you are solving for it, enter the future value. That is the balance you want after the last period. For a loan you pay off in full it is 0.
- Read the result. It updates as you type, so there is no button to press. Next to the solved amount you get the total of the payments and the total interest. When you solve for periods you get the number of periods and the same span in years.
The formula and its conventions
FV = PV × (1 + i)^N + PMT × ((1 + i)^N − 1) ÷ i i = annual rate ÷ periods per year At a rate of 0: FV = PV + PMT × N
The calculator follows one balance from the present value to the future value. The annual rate is a nominal rate. Each period earns the annual rate divided by the periods per year, so 6% with 12 periods per year is 0.5% per period. Payments happen at the end of each period, after that period's interest. A positive payment adds to the balance and a negative payment takes from it. Present value and future value are balances and have to be 0 or more. To solve for the present value, the payment or the number of periods, the calculator rearranges the same equation.
Worked example
These are example numbers. You have $10,000 and add $200 at the end of every month for 10 years at 6% a year. Choose Future value, then enter a present value of 10,000, a payment of 200, 120 periods, a rate of 6 and 12 periods per year. The future value is $50,969.84. That is the $10,000.00 you started with, $24,000.00 in payments and $16,969.84 in interest. These are the calculator's default inputs, so you can check each figure above.
Three more examples
Each one uses example numbers and 12 periods per year. Type them in to follow along.
A loan payment
You borrow $25,000 for 60 months at 6%. Solve for Payment with a present value of 25,000, a future value of 0, 60 periods and a rate of 6. The payment is -$483.32 per period. It is negative because it takes money out of the balance. The total of payments reads -$28,999.20 and the total interest $3,999.20.
A balance that funds a monthly withdrawal
You want to take out $1,000 a month for 25 years from a balance that earns 5%, and end at 0. Solve for Present value with a payment of -1,000, a future value of 0, 300 periods and a rate of 5. You need $171,060.05 at the start. The remaining $128,939.95 of the $300,000 you take out is interest.
The rate on a loan or a savings plan
You borrow $25,000 and pay $483.32 a month for 60 months. Solve for Rate (I/Y) with a present value of 25,000, a payment of -483.32, a future value of 0 and 60 periods. The annual rate is 6%, or 0.5% per period and 6.1678% a year with the months compounded. For savings, $10,000 plus $200 a month that grows to $50,000 in 120 months earned 5.7267% a year.
Time to reach a target
You start at 0 and save $500 a month at 7%. Solve for Periods with a present value of 0, a payment of 500, a future value of 1,000,000 and a rate of 7. The answer is 436.52 periods, or 36.38 years. The balance passes $1,000,000 during period 437.
Frequently asked questions
How do I solve for the rate, the I/Y on a TVM calculator?
Choose Rate (I/Y) and enter the present value, the payment, the future value and the number of periods. Money that leaves the balance, like a loan payment, is negative, and the answer is the nominal annual rate. There is no closed formula for it, so the calculator searches from 0% to 100% a year and tells you if no rate in that range fits. Under the result it shows the future value at the rate as printed, so you can see how close the 4 decimals land.
What is a finance calculator?
It is a calculator for time value of money. Five numbers describe a savings plan or a loan: present value, future value, payment, number of periods and interest rate. Give this calculator any four, and it works out the one that is missing.
What do PV, FV, PMT and N mean?
PV is the present value, the balance at the start. FV is the future value, the balance after the last period. PMT is the payment added or taken out each period. N is the number of periods. A period is the interval you pick under Periods per year, for example a month when you choose 12.
Why is my loan payment negative?
The calculator tracks one balance. A loan starts with the amount you owe as the present value and ends at a future value of 0. The payment has to bring the balance down, so it comes out negative. Read -$483.32 as a payment of $483.32 per period.
Does it compound monthly or yearly?
It compounds once per period, and you choose how many periods a year has: 1, 2, 4, 12, 24, 26, 52 or 365. With 12 periods per year both the payments and the compounding are monthly. The calculator cannot mix the two, such as monthly payments with daily compounding.
Are payments made at the start or the end of a period?
At the end. Each period first earns interest on the balance, and then the payment is added or taken out. A standard loan payment works this way. Payments at the start of each period, such as rent paid in advance, give a different result, and this calculator does not cover them.
What happens when the numbers do not work?
The calculator tells you why instead of showing a figure. Take a loan payment that is smaller than the interest added each period. The balance grows and never reaches 0, so there is no number of periods to show. You also get a message past its limits, which are amounts up to one trillion, rates from 0% to 100% and whole periods from 1 to 1,200. Present value and future value cannot be negative, though the payment can. A result above $50 trillion gets a message too, even when every entry is inside those limits.