Finding the future value of an annuity

A stream of equal periodic deposits compounded over time. Pin n to match the deposit frequency, then plug into the annuity formula.

01 Worked Example Video

Every step of Finding the future value of an annuity explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE

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.

Austin's tutoring center

Austin buys an annuity with a $104 quarterly payment at 3% compounded quarterly for 7 years. Payments are made at the end of each quarter.

What’s the total value of the annuity after 7 years? Type just the number, rounded to the nearest cent.

Do not round intermediate computations.

A = $

Lisa's down-payment fund

Lisa buys an annuity with a $200 monthly payment at 4.8% compounded monthly for 5 years. Payments are made at the end of each month.

What’s the total value of the annuity after 5 years? Type just the number, rounded to the nearest cent.

Do not round intermediate computations.

A = $

Diego's small business

Diego buys an annuity with a $300 semiannual payment at 6% compounded semiannually for 10 years. Payments are made at the end of each half-year.

What’s the total value of the annuity after 10 years? Type just the number, rounded to the nearest cent.

Do not round intermediate computations.

A = $

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

A = M[(1 + r/n)^nt − 1] / (r/n) M is per-period deposit

Match n to the deposit schedule quarterly → n = 4, monthly → n = 12

An annuity is a stream of equal deposits that compound over time. Match n to how often deposits happen. Then the exponent is n × t, not just t. Compute the bracket first, subtract 1, divide by r/n, multiply by M. See it live: watch the interest band balloon on a $200 monthly deposit at 8% →

Common slips

(1) Used t instead of nt as the exponent. For quarterly over 7 years, the exponent is 28, not 7. (2) Used r instead of r/n. The per-period rate is r/n — 0.03/4 = 0.0075, not 0.03. (3) Forgot to subtract 1. The bracket is (1 + r/n)^nt minus 1. Skipping the subtraction inflates the answer roughly 5×.

04 Practice — Step by Step

Practice this problem step by step

Deposit $200 per quarter into an annuity paying 8% compounded quarterly for 5 years. What’s the future value?

Step 1

Pick n

The deposits are quarterly. What’s n?

Step 2

Pick the exponent nt

With n = 4 and t = 5 years, what’s the exponent nt?

Step 3

Plug into the formula

With M = 200, r/n = 0.02 (= 0.08/4), and nt = 20, compute A = 200 × [(1.02)²⁰ − 1] / 0.02. (1.02)²⁰ ≈ 1.485947. Round to the nearest cent.

A = $

Q5 Topic overview

Finding the future value of an annuity

You walked the annuity formula end to end.