Comparing simple and compound interest year by year

Two identical deposits, two identical rates, one compounding and one not. The surprise is that year one is a dead heat.

01 Worked Example Video

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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.

Year two

$12,000 at 4% compounded annually.

How much interest is earned in the second year? Type just the number.

The tie

Two people each deposit $3,500 at 7%. One account compounds annually, the other is simple interest.

How much interest does the compound account earn in the first year? Type just the number.

Year three

$5,000 at 8% compounded annually.

How much interest is earned in the third year? Type just the number.

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 = P × r same every year, forever

compound: interest = (current balance) × r the base grows, so the interest grows

Simple interest is always charged on the original deposit. Compound interest is charged on whatever is in the account right now, which includes interest already earned. In year one those are the same number, because nothing has been earned yet.

Common slips

(1) Picking the compound account for year one. They tie. (2) Reporting the balance instead of the interest. The table asks what was earned that year, not the running total. (3) Growing the simple account. Its base never moves off the original deposit.

04 Practice — Step by Step

Year one is a tie

Nadia deposits $8,000 into an account paying 5% per year, compounded annually.

Omar deposits $8,000 into an account that also pays 5% per year, but it is simple interest.

Find the interest each earns during each of the first three years, and decide who earns more each year. Assume no withdrawals and no additional deposits.

Step 1

Year 1 — Omar (simple)

5% of the original $8,000.

Step 2

Year 1 — Nadia (compound)

Her account has $8,000 in it at the start of year one. What does she earn?

Step 3

Year 1 — who earns more?

Both earned $400. So who comes out ahead in the first year?

Step 4

Year 2 — Nadia

Her balance is now 8,000 + 400 = $8,400. What does she earn in year two?

Step 5

Year 3 — Nadia

Her balance is now 8,400 + 420 = $8,820. Year three?

Exam 2 Review Q2

Comparing simple and compound interest year by year

The gap opens in year two, not year one