Lesson 14 of 1524
Money management
Simple interest stays on the original principal. Compound interest pays interest on interest.
Practice this chapterA discount or a tax is a percent of a price, which is the percent skill from the foundations. Interest adds time.
Simple interest is I = Prt, always on the original principal. Annual compound growth is A = P(1 + r)^t. The (1 + r) is multiplied by itself once for each year.
Two interest models
I = Prt and A = P(1 + r)^t
Simple interest is the interest alone. Compound growth is the new total.
Worked example
$100 grows at 10% compounded annually for 2 years. What is it worth?
- 1The formula for the new total is A = P(1 + r)^t. It is not I = Prt, which would give only the simple interest.
- 2P = 100, r = 0.10, and t = 2, so 1 + r = 1.10 and A = 100 × (1.10)².
- 3(1.10)² means 1.10 × 1.10, which is 1.21. The exponent is two multiplications, not 1.10 × 2.
- 4100 × 1.21 = 121.
- 5Simple interest on the same loan would be I = 100 × 0.10 × 2 = 20, for a total of 120. The extra dollar is the second year of interest on the first year’s $10.
Result: $121
Why. Each year multiplies the whole balance by 1.10. After two years the growth factor is 1.21, so $100 becomes $121. The exponent is why the second year earns interest on more than the original $100.
I = Prt gives the interest, not the total in the account. The total after simple interest is P + I.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.