Future value of an annuity

Same amount deposited every year, every deposit earning interest for however long it has left. One formula does all of it at once.

01 Worked Example Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Fifteen years

$2,000 deposited at the end of each year into an annuity paying 5% compounded annually, for 15 years.

Find the total value. Type just the number.

Thirty years, small deposit

$500 a year at 8% compounded annually, for 30 years.

Find the total value. Type just the number.

Spot the wrong formula

$2,000 a year, 5%, 15 years — the same as version 1.

A student answered $4,157.86. What did they compute instead? Type the value of 1.05¹⁵ to four decimals.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 The Rule

FV = PMT × [((1 + i)ⁿ − 1) ÷ i] the annuity formula

annual deposits, annual compounding → i = r, n = years nothing to divide, nothing to multiply

The bracket is the annuity factor — what one dollar a year grows into over n years. Work it out on its own, then multiply by the deposit. Trying to key the whole expression in one go is where the bracket errors come from.

Common slips

(1) Using the compound interest formula. PMT × (1 + i)ⁿ treats it as one deposit sitting there, not a deposit every year. (2) Forgetting to subtract 1 in the numerator. (3) Rounding the factor. It routinely runs to two decimal places before the decimal point; chopping it moves the answer by dollars.

04 Practice — Step by Step

Build the factor, then multiply

Devon deposits $900 each year into an annuity paying 6% interest, compounded annually. Payments are made at the end of each year.

Find the total value of the annuity in 20 years.

Do not round any intermediate computations. Round your final answer to the nearest cent.

Step 1

What are i and n?

Annual deposits, compounded annually, for 20 years at 6%.

Step 2

The growth term

Compute (1.06)²⁰. Give four decimal places.

Step 3

The annuity factor

Subtract 1, then divide by 0.06. Give two decimal places.

Step 4

The total value

Multiply by the $900 annual deposit.

Step 5

How much did he actually deposit?

$900 a year for 20 years.

Q3 Q5

Future value of an annuity

Almost half of it is interest