Future Value Calculator

Calculate the future value of present money invested at a specific interest rate.

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What is Future Value?

Future Value (FV) is the value of a current asset at a specified date in the future, based on an assumed rate of growth.

Future Value is calculated by multiplying the present value by (1 + interest rate)^time period, which accounts for compound growth over time.

Understanding Future Value helps investors plan for long-term financial goals and evaluate the growth potential of investments.

The concept demonstrates how money can grow over time through the power of compound interest, where earnings generate additional earnings.

Future Value calculations are essential for retirement planning, education funding, and other long-term financial objectives.

The interest rate used in Future Value calculations can represent various types of returns, including savings account interest, investment returns, or inflation rates.

Future Value assumes that the interest rate remains constant over the entire time period and that all interest is reinvested.

Future Value Formula

\begin{gather*}\bold{Given{:}}\newline\begin{aligned}\text{Present Value} &= \mathrm{PV}\newline\text{Interest Rate} &= \mathrm{r}\newline\text{Time Period in Years} &= \mathrm{t}\end{aligned}\newline\bold{Calculate{:}}\newline\text{Future Value} = \mathrm{FV} \newline = \mathrm{PV} \times (1 + \frac{\mathrm{r}}{\mathrm{100{\%}}})^{\mathrm{t}}\end{gather*}

Future Value Calculation Examples

Example 1

An investor deposits $5,000 in a savings account that earns 6% annual interest, compounded annually. How much will this investment be worth after 5 years?

To calculate the future value:

\begin{gather*}\bold{Given{:}}\newline\begin{aligned}\text{Present Value}\space(\mathrm{PV}) &= \mathrm{{\$}5{,}000}\newline\text{Interest Rate}\space(\mathrm{r}) &= \mathrm{6{\%}}\newline\text{Time Period in Years}\space(\mathrm{t}) &= 5\end{aligned}\newline\bold{Calculate{:}}\newline\text{Future Value}\space(\mathrm{FV})\newline\begin{aligned}&= \mathrm{PV} \times (1 + \frac{\mathrm{r}}{\mathrm{100{\%}}})^{\mathrm{t}}\newline&= \mathrm{{\$}5{,}000} \times (1 + \frac{\mathrm{6{\%}}}{\mathrm{100{\%}}})^{5}\newline&= \mathrm{{\$}5{,}000} \times (1 + 0.06)^{5}\newline&= \mathrm{{\$}5{,}000} \times 1.06^{5}\newline&= \mathrm{{\$}5{,}000} \times 1.338\newline&= \mathrm{{\$}6{,}691.128}\end{aligned}\end{gather*}

The future value is $6,691.128, meaning that the initial investment of $5,000 will grow to $6,691.128 after 5 years at 6% annual interest.

The investment will earn $1,691.128 in interest over the 5-year period due to the power of compound growth.

Example 2

A young professional invests $25,000 in a retirement account that earns an average annual return of 4%. What will this investment be worth in 15 years?

Let's calculate the future value of this long-term investment:

\begin{gather*}\bold{Given{:}}\newline\begin{aligned}\text{Present Value}\space(\mathrm{PV}) &= \mathrm{{\$}25{,}000}\newline\text{Interest Rate}\space(\mathrm{r}) &= \mathrm{4{\%}}\newline\text{Time Period in Years}\space(\mathrm{t}) &= 15\end{aligned}\newline\bold{Calculate{:}}\newline\text{Future Value}\space(\mathrm{FV})\newline\begin{aligned}&= \mathrm{PV} \times (1 + \frac{\mathrm{r}}{\mathrm{100{\%}}})^{\mathrm{t}}\newline&= \mathrm{{\$}25{,}000} \times (1 + \frac{\mathrm{4{\%}}}{\mathrm{100{\%}}})^{15}\newline&= \mathrm{{\$}25{,}000} \times (1 + 0.04)^{15}\newline&= \mathrm{{\$}25{,}000} \times 1.04^{15}\newline&= \mathrm{{\$}25{,}000} \times 1.801\newline&= \mathrm{{\$}45{,}023.588}\end{aligned}\end{gather*}

The future value is $45,023.588, showing that the initial investment of $25,000 will grow to $45,023.588 over 15 years at 4% annual return.

This demonstrates the significant impact of time and compound growth on long-term investments, with total growth of $20,023.588 over the investment period.

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