Calculating and comparing simple interest and compound interest

Two accounts, same principal, same rate, three years. One simple, one compound. Watch the gap open up.

01 Worked Example Video

Every step of Calculating and comparing simple interest and compound interest 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.

Karen vs. David

Karen and David each deposit $80,000 into accounts paying 6% per year. Karen’s pays simple; David’s is compounded annually. After 3 years, how much more total interest did David earn than Karen?

extra = $

Anna vs. Brian

Anna and Brian each deposit $50,000 into accounts paying 4% per year. Anna’s is simple; Brian’s is compounded annually. After 3 years, how much more total interest did Brian earn?

extra = $

Marco vs. Lena

Marco and Lena each deposit $100,000 into accounts paying 5% per year. Marco’s is simple; Lena’s is compounded annually. After 3 years, how much more total interest did Lena earn?

extra = $

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

Simple: interest each year always P × r — never changes

Compound: interest each year (current balance) × r — grows

Simple interest only multiplies the original principal. Compound interest multiplies the most-recent balance — so last year’s interest earns interest this year. That’s the whole engine. See it live: simple vs. compound at $2,000, 5%, 3 years →

Common slips

(1) Used the original balance every year for compound. If your compound Year 2 matches Year 1, you’ve described simple interest — the compound principal has to grow. (2) “Compound wins Year 1.” Year 1 is always a tie: both formulas earn P × r. Compound only pulls ahead starting Year 2.

04 Practice — Step by Step

Practice this problem step by step

Two accounts, each $2,000 at 5%, held for 3 years. One earns simple interest, the other compounded annually. How much more does compound earn?

Step 1

Simple side — Year 1 interest

Simple account: interest each year is always P × r. Compute one year’s interest.

I_each = $

Step 2

Simple side — 3-year total interest

$100 each year × 3 years. Total simple interest?

simple I_total = $

Step 3

Compound side — end of Year 1

Compound account: Year 1 always ties simple ($100 interest). What’s the balance at the end of Year 1?

balance = $

Step 4

Compound side — end of Year 2

Year 2 interest = $2,100 × 0.05. Add to $2,100 for the new balance.

balance = $

Step 5

Compound side — end of Year 3

Year 3 interest = $2,205 × 0.05. Add to $2,205 for the final balance.

balance = $

Step 6

The gap

Compound total interest = $315.25. Simple total interest = $300. How much more did compound earn?

extra = $

Q14 Q16

Calculating and comparing simple interest and compound interest

You walked both sides end to end.