Interest – Simple and Compound
Interest is the cost of borrowing money, or the reward for saving it. Whether you are taking out a loan, putting money in a bank, or investing, interest calculations are built on percentage maths.
Simple Interest
Simple Interest (SI) = (Principal times Rate times Time) / 100. Where: P = the amount of money borrowed or saved, R = annual interest rate as a percentage, T = time in years.
Worked Examples - Simple Interest
SI = (500 times 4 times 3) / 100 = 6000 / 100 = 60. Total amount = 500 + 60 = 560.
SI = (1200 times 5 times 2.5) / 100 = 15000 / 100 = 150. Total repaid = 1350.
Compound Interest
Compound interest means interest is calculated on the growing total each period, not just the original principal. This makes money grow faster.
Amount = Principal times (1 + Rate/100) raised to the power of n. Where n = number of years (or compounding periods). Compound Interest = Amount minus Principal.
Worked Examples - Compound Interest
Year 1: 1000 times 1.10 = 1100. Year 2: 1100 times 1.10 = 1210. Year 3: 1210 times 1.10 = 1331. CI = 1331 - 1000 = 331. (Simple interest would have been only 300.)
Amount = 2000 times (1.05)^4 = 2000 times 1.2155 = 2431.01. CI = 2431.01 - 2000 = 431.01.
Simple vs Compound Interest
| Simple Interest | Compound Interest | |
|---|---|---|
| Based on | Original principal only | Growing total each period |
| Formula | P times R times T / 100 | P times (1+R/100)^T - P |
| Growth | Linear | Exponential |
| Best for | Short-term loans | Long-term savings / investments |
Key Takeaways
- Simple interest: always calculated on the original principal.
- Compound interest: calculated on the total (principal plus interest so far) each period.
- Compound interest always gives a larger total than simple interest for the same rate and time.
- The multiplier method: raise (1 + R/100) to the power of the number of years.
Practice Questions
- Find the simple interest on 800 at 6% per year for 4 years.
- A loan of 2500 charges 8% simple interest per year. How much is owed after 18 months?
- Find the compound interest on 3000 at 5% per year for 2 years.
- How much does 500 grow to after 10 years at 3% compound interest per year?
- Which gives more after 5 years on 1000: 10% simple interest or 8% compound interest?