How can compound interest be derived from simple interest?

Answer 1

Compound interest is simply simple interest except the amount of interest you owe is always added into the amount of money you borrowed before you calculate.

Lets give an example.

You borrowed a million from the bank at Year 2000 with interest rates of 5%.

The formula for simple interest is PIN/100, where P is Principle (amount owed), I is interest rate (in percentage), N is the number of years.

Year 2000: 1,000,000

Year 2001: 1,000,000 * 5 * 1 / 100 = 50,000 (this is the interest)

Year 2002: (1,000,000 + 50,000) * 5 * 1 / 100 = 52,500

By the end of 2002, you would owe the bank 1,102,500(1,000,000 + 50,000 + 52,500)

The formula for compound interest is P * (1 + I/100)N where P,I and N still refers to the same thing.

Year 2000: 1,000,000

Year 2001: 1,000,000 * (1+5/100)1 = 1,050,000

Year 2002: 1,050,000 * (1+5/100)1 = 1,000,000 * (1+5/100)2 = 1,102,500