Review · Q4 · Finding the future value and interest for an investment earning compound interest

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.

David's CD v1

David received a $2,100 bonus. He decided to invest it in a 2-year certificate of deposit (CD) with an annual interest rate of 1.15% compounded annually.

(a) Assuming no withdrawals are made, how much money is in David's account after 2 years?
(b) How much interest is earned on David's investment after 2 years?

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

Maria's CD v2

Maria received a $5,000 bonus. She decided to invest it in a 3-year certificate of deposit (CD) with an annual interest rate of 2.4% compounded annually.

(a) Assuming no withdrawals are made, how much money is in Maria's account after 3 years?
(b) How much interest is earned on Maria's investment after 3 years?

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

Jamal's CD v3

Jamal received a $1,800 bonus. He decided to invest it in a 4-year certificate of deposit (CD) with an annual interest rate of 1.8% compounded annually.

(a) Assuming no withdrawals are made, how much money is in Jamal's account after 4 years?
(b) How much interest is earned on Jamal's investment after 4 years?

Do not round any intermediate computations, and round your final answers 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 = P(1 + r/n)^nt
(annual compounding: n = 1)

When n = 1, the formula collapses to A = P(1 + r)^t — no fraction inside the parentheses.

1

Name the four pieces.

P = $2,100, r = 0.0115 (1.15% as a decimal), n = 1 (annual), t = 2 years.

2

Compute the future value (part a).

Plug into the formula. Compute the parenthesis first, raise to the 2nd power, then multiply by P.

A = 2,100 \times (1 + 0.0115) 2 = 2,100 \times (1.0115) 2 = 2,100 \times 1.02313225 = $2,148.58

Don't round 1.02313225 — carry the full decimal until the final answer.

3

Compute the interest (part b).

Subtract the original principal from the future value. Use the un-rounded A (2148.577725) for the subtraction, then round once at the end.

I = A - P = 2,148.577725 - 2,100 = $48.58

Visualizing the growth: the principal stays the same height; the interest band sits on top and grows slightly faster each year (year 2 added $24.43 vs. year 1's $24.15 — interest earned interest).

▸ COMMON SLIPS(1) Rounded too early. If you rounded 1.02313225 to 1.0231 before multiplying, you'd get $2,148.51 instead of $2,148.58 — a real difference. (2) Used 1.15 instead of 0.0115. 1.15% as a decimal is 0.0115 — shift two places left, not one. (3) Confused A and I. Part (a) asks for the full account balance ($2,148.58); part (b) asks for interest alone ($48.58).

04 Practice — Step by Step

Try the same shape with different numbers. Round to the nearest cent.

1

Future value with annual compounding.

$5,000 invested in a 3-year CD at 2.5% compounded annually. What's the balance after 3 years?

A = $

2

Continuous compounding variant.

Same idea, different formula: $1,000 at 4% compounded continuously for 5 years. Find A.

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.