Compound versus Simple Interest
Algebra
Explore how compound interest grows compared with simple interest, and where the two diverge.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Simple interest pays the same fixed amount every year. Compound interest pays interest on the interest already earned, so the balance grows faster the longer it is left. Few UK savings accounts still offer simple interest, which is itself a clue about which one suits the bank better. This exploration compares the two models properly: where they cross over, how well the 'rule of 72' holds up, and what happens as compounding gets more frequent than once a year.
Guiding Questions
- Write formulas for a savings account under simple and under compound interest.
- After how long does compound interest overtake simple interest for realistic rates? Solve and graph it.
- How long does money take to double at different rates? Test the 'rule of 72' against your calculations.
- Find a real savings product and work out what its advertised rate pays out over 10 years.
- Write the balance formula for n compounding periods a year, then let n grow without bound. What does the formula turn into, and why does that connect compound interest to the number e?