Determine present and future values

Present value and future value describe the equivalent worth of money at different times: a future amount is obtained by compounding a present amount forward, while present value is found by discounting a future amount back using a stated interest rate, compounding frequency, and number of periods. The relationships are represented with formulas such as $F=P(1+i)^n$ and applied to lump sums and regular payment streams, with careful alignment of the rate and time period; continuous compounding and more advanced cash-flow models are outside this scope.

Detailed Explanation: Determine present and future values

To determine present value or future value, first make sure the interest rate and number of periods match the compounding frequency.

For compound interest:

F=P(1+i)^n

where:

$F$ is the future value
$P$ is the present value
$i$ is the interest rate per compounding period
$n$ is the total number of compounding periods

Example

An account earns $6\%$ annual interest compounded quarterly.

Find the future value of 2{,}000$ after 3 years.
Find the present value of 2{,}500$ due in 3 years.

Step 1: Convert the rate and time

Because interest is compounded quarterly, there are 4 periods per year.

The rate per quarter is:

i=\frac{0.06}{4}=0.015

The total number of quarters is:

n=3(4)=12

Part 1: Find the future value

Use:

F=P(1+i)^n

Substitute the known values:

F=2000(1.015)^{12}

Calculate:

F\approx \$2{,}391.24

So, 2{,}000 $will grow to approximately **$ $2{,}391.24$** after 3 years.

Part 2: Find the present value

To find the amount needed today for a future amount, rearrange the formula:

P=\frac{F}{(1+i)^n}

Substitute the values:

P=\frac{2500}{(1.015)^{12}}

Calculate:

P\approx \$2{,}090.61

Therefore, the present value of 2{,}500 $due in 3 years is approximately **$ $2{,}090.61$**.

Remember: use multiplication to move money forward to its future value, and division to move money backward to its present value.

Learn by doing: Determine present and future values

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

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