Determine future value of an investment

Future value is the accumulated amount of an investment after interest or growth over time, determined from the principal, interest rate, compounding frequency, and duration using simple- or compound-interest models. The calculation requires matching the rate and number of periods to the compounding interval and interpreting compound growth as interest earned on previously accumulated interest; it supports exponential functions and financial decision-making, but excludes continuously varying rates, irregular deposits or withdrawals, inflation adjustments, taxation, and other advanced investment models.

Detailed Explanation: Determine future value of an investment

Future value is the amount an investment grows to after earning interest. For compound interest, use

A=P\left(1+\frac{r}{n}\right)^{nt}

where:

$A$ is the future value,
$P$ is the principal, or starting amount,
$r$ is the annual interest rate written as a decimal,
$n$ is the number of times interest is compounded per year,
$t$ is the time in years.

Example

You invest 1{,}200 $at an annual interest rate of$ 5.4% $, compounded monthly, for$ 3$ years. What is the future value?

Step 1: Identify the values.

P=1200,\qquad r=0.054,\qquad n=12,\qquad t=3

The rate is written as a decimal because $5.4\%=0.054$ . Since interest is compounded monthly, there are $12$ compounding periods per year.

Step 2: Substitute into the formula.

A=1200\left(1+\frac{0.054}{12}\right)^{12(3)}

Step 3: Simplify the rate and number of periods.

A=1200(1+0.0045)^{36}

The monthly interest rate is $0.0045$ , or $0.45\%$ , and there are $36$ monthly periods in $3$ years.

Step 4: Calculate.

A=1200(1.0045)^{36}\approx 1410.45

Therefore, the investment’s future value is approximately

\boxed{\$1{,}410.45}

The investment earned approximately 210.45$ in interest:

1410.45-1200=\$210.45

Always match the rate and number of periods to the compounding interval. For monthly compounding, divide the annual rate by $12$ and multiply the number of years by $12$ .

Learn by doing: Determine future value of an investment

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Exponential Function Solving - Compound Interest (Discrete) Scenario to Value at Time

Earned ?