Lessons · Engineering · simple and compound interest
Interest: simple grows in a line, compound grows on itself
Simple interest is I = P × i × n. Compound interest grows the whole sum each period: F = P × (1 + i)ⁿ.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
Two quotes for the same machine, one with a loan at 6 % simple and one at 5.5 % compound. Which costs less over five years is not obvious from the rates, and the person who can work it out in the meeting is the one who gets asked to the next one.
How to think about it
Turn the percent into a fraction: 5 % is 0.05. Simple: principal times rate times years. Compound: principal times (1 + rate) to the power of the years. The difference between the two is interest on interest.
Worked example
Simple: I = P × i × n. Compound: F = P × (1 + i)ⁿThe two rules. i is a fraction, n is the number of periods.
$8,000 at 5 % for 4 years, simple: I = 8000 × 0.05 × 4 = $1,600Same interest every year, four years of it.
Compound: F = 8000 × 1.05⁴ = 8000 × 1.2155 = $9,724; interest $1,724Each year's interest joins the principal for the next.
The extra $124 is interest on interestSmall over four years. Over thirty it is most of the money.
Your turn
$2,000 at 4 % for 3 years, compound. Write the future sum.
F = 2000 × (1 + )³ = $2,249.73
Solve one, graded on the server
The trap
Using 5 instead of 0.05. 8000 × 5 × 4 is $160,000 of interest on an $8,000 loan, and the arithmetic alone will not tell you that is absurd. The rate is a fraction.