Compound Interest

About this video

Compound interest — interest on the interest — with the formula A = P(1 + i)ⁿ, the rate going in over 100 (15% is 15 over 100): finding the future value and the interest earned, and working backwards to the amount first borrowed.

What it covers

Simple versus compound: compound grows on the previous value
The formula A = P(1 + i)ⁿ, with the rate written over 100
The future value A, and the interest A − P
Working backwards: divide by the bracket to find P
Typing it into the calculator in one go

Extra worked examples

✍️ Extra example: R12 000 is invested at 8% per year, compounded annually, for 5 years. Find the future value and the interest earned.

1
A = 12 000(1 + 8/100)⁵
P = R12 000, the rate is 8 over 100, n = 5 years.
2
A = R17 631,94
Calculator: 12 000 × ( 1 + 8 ÷ 100 ) ^ 5.
3
Interest = A − P = R17 631,94 − R12 000 = R5 631,94
A is what you HAVE; A − P is what you GAINED.

✍️ Extra example: how much must be invested now at 10% per year, compounded annually, to have R50 000 in 3 years?

1
50 000 = P(1 + 10/100)³
Now A (the end amount) is known and P is not.
2
P = (50 000)/(1 + 10/100)³
Almost like solving for x: divide both sides by the whole bracket.
3
P = R37 565,74
That is what must be invested now.

Exercises to try

Work each one out, then click to reveal the answer.

1
R2 000 is invested at 6% per year, compounded annually, for 4 years. What is it worth then?
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A = 2 000(1 + 6/100)⁴ = R2 524,95
2
R5 000 is invested at 12% per year, compounded annually, for 2 years. How much interest is earned?
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A = 5 000(1 + 12/100)² = R6 272; interest = R6 272 − R5 000 = R1 272
3
R10 000 is invested for 3 years at 10% per year. Compare simple and compound interest.
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Simple: SI = (10 000 × 10 × 3) ÷ 100 = R3 000 → R13 000. Compound: 10 000(1 + 10/100)³ = R13 310. Compound earns R310 more.
4
What must be invested at 8% per year, compounded annually, to grow to R20 000 in 2 years?
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P = (20 000)/(1 + 8/100)² = R17 146,78
5
A loan of R80 000 grows at 15% per year, compounded annually. What is owed after 2 years if nothing is paid?
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A = 80 000(1 + 15/100)² = R105 800

Read the full lessons

💰Grade 9 · Whole NumbersFinancial Maths: Interest, Hire Purchase & Exchange Rates 💰Grade 10 · Finance and GrowthSimple & Compound Interest: The Grade 10 Question Types

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