Lecture video
Walkthrough of the Module 5 interest concepts.
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1 · Simple vs. compound interest
Simple interest is paid only on the original principal:
I = P · r · t (principal × annual rate × years)
Compound interest is paid on the principal and on interest already earned, so the balance grows faster:
A = P (1 + r/n)n·t
where n is the number of compounding periods per year (12 for monthly, 4 for quarterly, 1 for annual). The more often it compounds, the more you earn.
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2 · APR vs. APY
APR (annual percentage rate) is the stated yearly rate. APY (annual percentage yield) is the rate you actually earn once compounding is included — so APY is a little higher than APR whenever interest compounds more than once a year. When comparing accounts, compare APYs.
Worked Examples
See it done, step by step
Example 1 — $2,000 at 4% simple interest for 3 years
Use I = P · r · t, then add the interest to the principal.
I = 2000 × 0.04 × 3 = $240.
Total balance = 2000 + 240 = $2,240.
Example 2 — $2,000 at 4% compounded annually for 3 years
Use A = P(1 + r/n)n·t with n = 1.
A = 2000 (1.04)3 = 2000 × 1.124864 ≈ $2,249.73.
That's about $9.73 more than simple interest — the effect of compounding.
Example 3 — $5,000 at 3% compounded monthly for 2 years
Here r/n = 0.03/12 = 0.0025 and n·t = 24.
A = 5000 (1.0025)24 ≈ 5000 × 1.06176 ≈ $5,308.81.
Watch & Review
Resources for this module
Lecture slides
The Module 5 slides on interest and compounding.
Open slidesCalculators
Check Yourself
Quick self-check
1. Find the simple interest on $1,500 at 5% for 2 years.
I = 1500 × 0.05 × 2 = $150.
2. Which earns more over time at the same rate — simple or compound interest?
Compound, because it also earns interest on previously earned interest.
3. When comparing two savings accounts, should you compare APR or APY?
APY — it reflects what you actually earn after compounding.
Ready to turn it in?
When you're confident with interest calculations, complete the Module 5 homework and quiz in Canvas.
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