Difference Between Compound and Simple Interest

Let's solve this problem involving compound and simple interest. We're given that for a certain sum of money at eight percent interest for two years, the compound interest exceeds the simple interest by seventy-six point eighty rupees.

Let's start by defining our variables. Let the principal sum be P, the rate r is eight percent per annum, and the time t is two years.

First, let's write the formula for Simple Interest, which is principal times rate times time divided by one hundred.

Substituting our values, eight for the rate and two for the time, we get simple interest is zero point sixteen times P.

Now, let's look at Compound Interest. The formula is the Principal times the quantity one plus r over one hundred to the power of t, minus the principal.

Plugging in the numbers, we have one plus eight over one hundred squared, minus one, all multiplied by P.

This simplifies to one point zero eight squared minus one. Squaring one point zero eight gives us one point one six six four.

So, the Compound Interest is zero point one six six four times P.

We are told the difference between Compound Interest and Simple Interest is seventy-six point eighty. Let's set up the equation.