Skip to content
CalculatorBuddy

Finance Calculator

A five-key time value of money calculator: solve for future value, present value, periodic payment, number of periods, or interest rate, with a full period schedule.

periods
%
$
$
/year

Compounding matches the payment frequency. Use 1 for annual, 12 for monthly.

Payment is made at the

of each period. Beginning-of-period payments earn one extra period of interest.

Future Value (FV)

-$9,455.36

Sum of Payments
-$20,000.00
Total Interest
$9,455.36

Period schedule

PeriodPaymentInterestBalance
Period 1-$2,000.00$1,200.00$19,200.00
Period 2-$2,000.00$1,152.00$18,352.00
Period 3-$2,000.00$1,101.12$17,453.12
Period 4-$2,000.00$1,047.19$16,500.31
Period 5-$2,000.00$990.02$15,490.33
Period 6-$2,000.00$929.42$14,419.75
Period 7-$2,000.00$865.18$13,284.93
Period 8-$2,000.00$797.10$12,082.03
Period 9-$2,000.00$724.92$10,806.95
Period 10-$2,000.00$648.42$9,455.36
Future Value (FV)-$9,455.36View results

Solve any one variable of a time-value-of-money problem. Enter the four values you know — number of periods, interest rate, present value, payment, or future value — pick the tab for the unknown, and the calculator solves it, just like a five-key financial calculator. Each result comes with the sum of payments, total interest, and a period-by-period schedule.

Formula

All five tabs rearrange one identity. For a per-period rate i (= I/Y ÷ 100 ÷ P/Y), N periods, and type = 1 for beginning-of-period payments (else 0):

PV × (1 + i)^N  +  PMT × (1 + i·type) × [ (1 + i)^N − 1 ] / i  +  FV  =  0

FV, PV, and PMT have direct closed-form rearrangements; N comes from a logarithm; the rate I/Y is found by numerical search.

Keep your signs consistent: money you pay out is one sign, money you receive is the other. If a result looks backwards, check the sign of PMT.

What each tab solves for

TabYou provideIt solves for
FVN, I/Y, PV, PMTthe future value
PMTN, I/Y, PV, FVthe periodic payment
I/YN, PV, PMT, FVthe annual rate
NI/Y, PV, PMT, FVthe number of periods
PVN, I/Y, PMT, FVthe present value

Examples

$20,000 today, withdraw $2,000/year for 10 years at 6%

With PV = $20,000, PMT = −$2,000, N = 10, and I/Y = 6%, the future value is −$9,455.36. The payments sum to −$20,000 and the account earns $9,455.36 in interest over the ten periods.

Solving for the rate

Switch to the I/Y tab and enter PV = $20,000, PMT = −$2,000, N = 10, FV = −$9,455.36; the calculator searches for and returns a 6% annual rate.

Frequently asked questions

What is the time value of money?
It is the idea that a dollar today is worth more than a dollar in the future, because today's dollar can be invested to earn a return. The five variables N, I/Y, PV, PMT, and FV describe a cash-flow stream over time, and knowing any four lets you solve for the fifth.
What do N, I/Y, PV, PMT, and FV mean?
N is the number of periods, I/Y is the interest rate per year, PV is the present value (a lump sum today), PMT is the level payment each period, and FV is the future value (a lump sum at the end). This works like a financial calculator such as the BA II Plus or HP 12C.
Why are some values negative?
Cash flows use signs: money coming to you is positive and money leaving you is negative (or vice versa, as long as you are consistent). A deposit or loan payment is typically entered as a negative PMT, and a resulting balance you would receive shows as the opposite sign.
What is the difference between beginning and end of period?
It sets when each payment occurs. End-of-period (an ordinary annuity) is the default. Beginning-of-period (an annuity due) means each payment is made one period earlier, so it earns one extra period of interest, which slightly changes the result.
How does it solve for the interest rate?
There is no algebraic formula for the rate, so the calculator searches for the rate that makes the time-value equation balance, narrowing the range until it converges — the same numerical approach a financial calculator uses.

Related calculators