Time Value of Money Calculator

Find the future value of a present sum plus regular contributions, using the standard compound-interest and annuity formulas.

Quick Facts

Formula
FV = PV(1+i)^n + PMT[((1+i)^n-1)/i]
i is the interest rate per compounding period and n is the total number of periods.
Model
Lump sum growth plus ordinary annuity contributions
Contributions are assumed to be made at the end of each compounding period.

Your Results

Calculated
Future value
-
Total value at the end of the term
Total contributions
-
Present value plus all periodic payments
Total interest earned
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Future value minus total contributions
Effective annual rate
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True annual yield from compounding

Ready

Enter a present value, rate, time period, compounding frequency, and contribution, then press Calculate.

How the Time Value of Money Calculator works

The time value of money is the idea that a dollar today is worth more than a dollar in the future, because money in hand can be invested and earn interest. This calculator quantifies that idea: it projects what a present sum, plus a stream of regular contributions, grows into after a chosen number of years at a given interest rate and compounding frequency.

The formula

The calculator combines two standard time-value-of-money building blocks — the future value of a lump sum and the future value of an ordinary annuity:

FV = PV × (1 + i)n + PMT × [((1 + i)n − 1) / i]

Here PV is the present value you enter, PMT is the contribution made at the end of each compounding period, i is the periodic interest rate (the annual rate divided by the number of compounding periods per year), and n is the total number of periods (years multiplied by periods per year). If the interest rate is 0%, the formula simplifies to FV = PV + PMT × n, since there is no growth to compound.

Worked example

Take a present value of $10,000, a 6% annual rate compounded monthly, a $200 monthly contribution, and a 10-year term. The periodic rate is 0.06 / 12 = 0.005 and n = 120 periods. The lump sum alone grows to about $18,194, and the contributions grow to about $32,776, for a future value of roughly $50,970. Total contributions over the period equal $10,000 + $200 × 120 = $34,000, so the remaining approximately $16,970 is interest earned purely from compounding.

Why compounding frequency matters

The same nominal annual rate produces a slightly larger future value the more often it compounds, because interest starts earning interest sooner. To compare rates with different compounding schedules on equal footing, the calculator also reports the effective annual rate (EAR): EAR = (1 + i)m − 1, where m is the number of compounding periods per year. A 6% nominal rate compounded monthly has an EAR of about 6.17%, slightly above the nominal figure.

What moves the future value most

  • Time: because growth compounds, extending the term has an outsized effect — the same inputs run for 20 years instead of 10 roughly double or more the interest earned, not just the total.
  • Interest rate: a higher rate increases both the lump-sum growth and the annuity growth, and the effect compounds each period.
  • Regular contributions: even modest periodic contributions can outweigh the lump sum over a long horizon, since each contribution has less time to compound than the ones before it but there are many of them.

Assumptions

This calculator assumes a fixed interest rate for the entire term, contributions of a constant amount made at the end of each compounding period (an ordinary annuity, not an annuity due), and no fees, taxes, or inflation adjustments. It is a computational tool, not personalized financial or investment advice — for decisions with real money at stake, verify results against your own account terms or a licensed professional.

Frequently Asked Questions

What formula does this Time Value of Money Calculator use?
It combines the future value of a lump sum with the future value of an ordinary annuity: FV = PV x (1+i)^n + PMT x [((1+i)^n - 1) / i], where PV is the present value, PMT is the contribution made at the end of each compounding period, i is the interest rate per period (annual rate divided by the number of compounding periods per year), and n is the total number of periods (years times periods per year).
How does compounding frequency change the future value?
More frequent compounding applies interest to a growing balance more often, so the same nominal annual rate produces a slightly higher future value as frequency increases from annual to monthly to daily. The effective annual rate (EAR = (1 + i)^m - 1, where m is periods per year) makes this comparable across frequencies.
What is the difference between total interest earned and total contributions?
Total contributions is simply the present value plus every periodic payment added over the term (PV + PMT x n). Total interest earned is the remainder of the future value after those contributions are removed (FV - total contributions) - it represents growth purely from compounding, not new money you put in.
Why is the effective annual rate different from the nominal annual rate?
The nominal annual rate is simply divided by the number of compounding periods to get the periodic rate. The effective annual rate accounts for interest earning interest within the year, so it is always equal to or higher than the nominal rate whenever compounding happens more than once a year.

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