Time Value of Money Calculator
Calculate present value and future value for lump sums and annuities. Supports all compounding frequencies.
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Compounding Growth Reference Table
Compounding growth shows how $1,000 grows at different interest rates and compounding frequencies over 10 years. This table illustrates why more frequent compounding produces higher returns.
| Rate | Annual | Quarterly | Monthly | Daily |
|---|---|---|---|---|
| 3% | $1,343.92 | $1,348.35 | $1,349.35 | $1,349.86 |
| 5% | $1,628.89 | $1,638.62 | $1,647.01 | $1,648.61 |
| 7% | $1,967.15 | $1,989.79 | $2,009.66 | $2,013.75 |
| 10% | $2,593.74 | $2,685.06 | $2,707.04 | $2,717.91 |
| 12% | $3,105.85 | $3,262.04 | $3,300.39 | $3,319.46 |
Based on a $1,000 investment over 10 years, compounded annually, quarterly, monthly, and daily.
What Is the Time Value of Money?
Time value of money (TVM) is the foundational principle that a dollar available today is worth more than the same dollar available in the future. The reason is opportunity cost: money available now can be invested to earn a return, making it grow into a larger amount over time. If you receive $1,000 today and invest it at 5% annual interest, it becomes $1,050 in one year. Waiting a year to receive the $1,000 costs you that $50 in potential earnings.
This principle underlies virtually every financial decision, from evaluating investment opportunities and valuing bonds, to setting loan terms, pricing insurance products, and comparing business projects. Understanding TVM allows you to make apples-to-apples comparisons between money amounts occurring at different points in time.
Present Value (PV)
Present value answers the question: what is a future sum of money worth in today’s terms? PV discounts a future amount back to the present using the interest rate as the discount rate. PV = FV / (1 + r/n)^(n·t)
Future Value (FV)
Future value answers: how much will a current amount grow to be? FV compounds a present amount forward through time using the interest rate. FV = PV × (1 + r/n)^(n·t)
Interest Rate (r)
The interest rate is the rate of return applied to the principal per year. It can represent investment growth, loan cost, or a discount rate for comparing cash flows across time periods.
Compounding (n)
Compounding frequency is how many times per year interest is calculated and added to the principal. More frequent compounding produces more total growth due to interest earning interest.
The Five TVM Variables
Every time value of money problem involves five variables: present value (PV), future value (FV), interest rate (r), time in periods (t), and number of compounding periods per year (n). When you know any four of these, you can solve for the fifth. This calculator solves for PV, FV, and annuity values given the other inputs.
Present Value and Future Value Formulas
Present value and future value formulas are the core equations used in every TVM calculation. Both derive from the same relationship between money and time.
Future Value Formula
FV = PV × (1 + r/n)^(n × t). In this formula, PV is the starting amount (present value), r is the annual interest rate as a decimal (so 5% becomes 0.05), n is the number of compounding periods per year, and t is the number of years. The expression (1 + r/n)^(n × t) is called the future value interest factor (FVIF).
Present Value Formula
PV = FV / (1 + r/n)^(n × t). This is simply the future value formula rearranged. The denominator (1 + r/n)^(n × t) serves as the discount factor. Dividing the future value by this factor converts it to a present-day equivalent. The discount factor increases over time, meaning money further in the future is worth less today.
Annuity Formulas
An annuity is a series of equal payments made at regular intervals. The present value of an ordinary annuity is PVA = PMT × [1 – (1 + r/n)^(–n × t)] / (r/n). The future value of an ordinary annuity is FVA = PMT × [(1 + r/n)^(n × t) – 1] / (r/n). In both formulas, PMT is the payment per period and the other variables are the same as above.
Frequently Asked Questions
The time value of money is the concept that a dollar available today is worth more than a dollar in the future, because today’s dollar can be invested to earn returns. This principle is the foundation of finance, investment valuation, and all loan and annuity calculations.
The present value formula is PV = FV / (1 + r/n)^(n × t), where FV is the future value, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years. It calculates how much a future amount is worth in today’s dollars.
The future value formula is FV = PV × (1 + r/n)^(n × t), where PV is the starting amount, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is years. It finds how much a current sum will grow to over time.
More frequent compounding produces a higher future value, because interest is earned on previously accumulated interest more often. $1,000 at 10% compounded monthly grows to about $2,707 over 10 years, compared to $2,594 with annual compounding. The difference becomes larger as the time period increases.
Present value (PV) is the current worth of a future sum discounted at a given interest rate. Future value (FV) is how much a current sum will grow to after earning interest. PV converts future money into today’s terms; FV converts today’s money into future terms. Both use the same formula rearranged.
An annuity is a series of equal payments made at regular intervals over a set time period. Common examples include monthly mortgage payments, lease payments, and retirement income distributions. An ordinary annuity has payments at the end of each period; an annuity due has payments at the beginning.
The discount rate for present value calculations depends on your purpose. For investment analysis, use your required rate of return or cost of capital. For loan analysis, use the loan’s interest rate. For comparing to a risk-free alternative, use a treasury bond yield. The rate reflects the minimum acceptable return given the risk of the cash flows.