Present & Future Value Algebra Calculator

Enter Calculation

Solve for Future Value (FV) Present Value (PV)

Known Amount (PV if solving FV, FV if solving PV)

Interest Rate per Period (%)

Number of Periods (n)

Results

Future Value

1,628.89

value of money over time

Growth Factor (1+r)ⁿ	1.628895
Total Interest / Difference	628.89

What This Calculator Does

The Present & Future Value Algebra Calculator applies the core time-value-of-money relationship between a sum today and the same money grown or discounted across time. It solves either direction of the compound-interest equation: turning a present value (PV) into a future value (FV), or discounting a future value back to its present value. This tool is universal arithmetic — it works for any currency and any compounding period (years, months, quarters) as long as the rate matches the period.

The Formula Explained

Future value is found with $$\text{FV} = \text{PV}(1 + r)^n$$ where r is the interest rate per period (as a decimal) and n is the number of periods. Rearranging algebraically to solve for the present value gives $$\text{PV} = \frac{\text{FV}}{(1 + r)^n}$$ The expression \((1 + r)^n\) is the compounding (or discounting) growth factor — each period multiplies the balance by \((1 + r)\), and raising it to the power \(n\) compounds that effect.

Compounding makes value grow exponentially as the number of periods increases.

Money grows from present value (PV) to future value (FV) by the factor \((1+r)^n\) over \(n\) periods.

How to Use It

First choose whether you are solving for Future Value or Present Value. Enter the known amount: if you want FV, this is your starting PV; if you want PV, this is the target FV. Enter the interest rate per period as a percentage (the tool converts it to a decimal), and the number of periods \(n\). The result shows the computed value, the growth factor \((1 + r)^n\), and the total interest or discount difference.

Worked Example

Invest $1,000 at 5% per year for 10 years. The growth factor is \((1.05)^{10} \approx 1.628895\). So $$\text{FV} = 1000 \times 1.628895 \approx \$1{,}628.89$$ meaning about $628.89 of compound interest is earned.

FAQ

Does the rate have to be annual? No. Use whatever period you like — just make sure \(r\) and \(n\) use the same period (e.g., a monthly rate with a number of months).

How do I convert an annual rate to monthly? Divide the annual percentage by 12 and use months for \(n\), assuming monthly compounding.

What if the rate is 0%? The growth factor becomes 1, so PV and FV are equal — money neither grows nor shrinks.