Suppose we want to know the expression/formula to find the total interest amount gained at the end of the maturity period. What would be the formula for each of the two options?

Question

Homi · Accepted Answer

We need to find the total interest for two options.

Step 1 — Simple Interest Formula Let us first understand simple interest. Simple interest is calculated only on the initial amount of money. Let P be the Principal (the initial amount of money). Let R be the Rate of Interest (percentage per year). Let T be the Time Period (in years). The interest for one year is $P \times \frac{R}{100}$ . For T years, the total simple interest is:

$\text{Simple Interest (SI)} = P \times \frac{R}{100} \times T$

$\text{SI} = \frac{P \times R \times T}{100}$

$\boxed{\text{Total Interest (Simple)} = \frac{P \times R \times T}{100}}$

Step 2 — Compound Interest Formula Now, let us look at compound interest. Compound interest earns interest on the principal. It also earns interest on past interest. Let P be the Principal (initial amount). Let R be the Rate of Interest (percentage per year). Let T be the Time Period (in years). First, we find the total amount after T years. The formula for the total amount (A) after T years is:

$A = P \left(1 + \frac{R}{100}\right)^T$

The total interest gained is the total amount minus the principal. So, the Compound Interest (CI) is:

$\text{Compound Interest (CI)} = A - P$

$\text{CI} = P \left(1 + \frac{R}{100}\right)^T - P$

$\text{CI} = P \left[ \left(1 + \frac{R}{100}\right)^T - 1 \right]$

$\boxed{\text{Total Interest (Compound)} = P \left[ \left(1 + \frac{R}{100}\right)^T - 1 \right]}$

Answer

(i) The formula for total Simple Interest is $\frac{P \times R \times T}{100}$ . (ii) The formula for total Compound Interest is $P \left[ \left(1 + \frac{R}{100}\right)^T - 1 \right]$ .

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