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 Mini-Lesson 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.

Austin's tutoring center v1

Austin wants to save money to open a tutoring center. He buys an annuity with a quarterly payment of $104 that pays 3% interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 7 years.

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

Lisa's down-payment fund v2

Lisa wants to save money for a house down payment. She buys an annuity with a monthly payment of $200 that pays 4.8% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 5 years.

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

Diego's small business v3

Diego wants to save money to launch a small business. He buys an annuity with a semiannual payment of $300 that pays 6% interest, compounded semiannually. Payments will be made at the end of each half-year. Find the total value of the annuity in 10 years.

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

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 How to Solve It

A = M[(1 + r/n)^nt − 1] / (r/n)

M is the periodic deposit. Match n to the deposit schedule — quarterly deposits with quarterly compounding means n = 4.

Name the four pieces.

M = $104 per quarter, r = 0.03 (3% annual as a decimal), n = 4 (quarterly), t = 7 years.

Compute the per-period rate and exponent.

Two preliminary numbers — both are easy to mis-key, so write them down.

r/n = 0.03 / 4 = 0.0075 n \times t = 4 \times 7 = 28 (quarters total)

Compute the parenthesis raised to the exponent.

This is the heaviest step on a calculator. Carry many decimal places.

(1 + 0.0075) 28 = (1.0075) 28 \approx 1.2327117476

Plug into the annuity formula.

Subtract 1 from the bracket result, divide by r/n, multiply by M.

A = 104 \times (1.2327117476 - 1) / 0.0075 = 104 \times 0.2327117476 / 0.0075 = 104 \times 31.0282330 = $3,226.94

Sanity check: total deposits = $104 × 4 × 7 = $2,912. Final balance is ~$3,227. The extra ~$315 is interest the annuity earned on its earlier deposits.

Visualizing it: contributions stack up linearly while the interest band curves above them, growing faster than the deposits as the early deposits compound longer.

▸ COMMON SLIPS(1) Used 7 as the exponent instead of 28. The exponent is n × t, not t. (2) Used 0.03 as r/n. r/n = 0.0075, not 0.03 — you have to divide by n. (3) Forgot to subtract 1. The bracket is (1+r/n)^(nt) − 1; if you skip the subtraction your answer comes out roughly 5× too big.

04 Practice — Step by Step

Try the annuity formula with different inputs.

Future value of a monthly annuity.

Monthly deposit of $50 at 4% interest compounded monthly for 10 years. What's the future value?

A = $

Annual annuity (different n).

Annual deposits of $500 at 5% compounded annually for 10 years. What's the future value?

A = $

▸ NICE WORK

You've walked through the whole problem.

That's the move. ALEKS will give you a different version with different numbers — but the steps are the same.

Q5 Topic overview