# Compound Interest

Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.” – Albert Einstein The formula for Compound interest is:

Total Amount = $\displaystyle\boxed{P(1+\frac{i}{100})^n}$

Where P=Principal amount (starting amount of money)

i = interest rate (in percent)

n = number of times compounded

We will illustrate this using an example:

## Compound Interest Example Question

Source: Admiralty Secondary School Preliminary Examination 2011 Paper 2

Q: The cash price of a sports car is $420,000. Mr Lionel buys it on compound interest loan terms. He pays a down payment of$300,000 and the balance at the end of 5 years with a compound interest rate of 5% per annum. Calculate the amount that Mr Lionel has to pay at the end of 5 years.

Solution:

Firstly, we have to find out what is the balance. The balance would be $420,000-$300,000=$120,000. That is the Principal amount, i.e. P=120,000. The interest rate, i=5. n=5 since the number of times compounded is 5 (once each year). Hence, Total Amount = $\displaystyle\boxed{P(1+\frac{i}{100})^n=120000(1+\frac{5}{100})^5=153153.79}$ In conclusion, he has to pay$153153.79 at the end of 5 years.

## How is Compound Interest the Eighth Wonder of the World?

Imagine you have an amount of $1000. (P=1000) And you manage to find a bank that pays 10% compound interest per annum. (i=10) What happens after 50 years? (n=50) Using the formula, Total Amount = $\displaystyle\boxed{P(1+\frac{i}{100})^n=1000(1+\frac{10}{100})^{50}=117390.85}$ The amount would become around$117,000! Isn’t it amazing? This is why Maths is useful and fun.

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