Question

A bank advertises that you can double the money if you invest it with them for $8$ years, what is the rate of interest offered by them?

Answer 1

Case $1:$ When the bank offers simple interest:

We know that

Simple Interest $\text{=}\frac{\mathrm{Principal}\mathrm{amount}\mathrm{x}\mathrm{Interest}\mathrm{Rate}\mathrm{x}\mathrm{Number}\mathrm{of}\mathrm{years}\mathrm{of}\mathrm{deposit}}{100}$

Simple Interest $\text{=}\frac{\mathrm{P}\mathrm{x}\mathrm{R}\mathrm{x}\mathrm{T}}{100}$

Let us assume Principal amount is $₹1000$

To make it double, interest earned has to be $₹1000$

By using the simple interest relation,

Interest Rate $\mathrm{=}\frac{\mathrm{Simple}\mathrm{Interest}\times 100}{\mathrm{Principal}\mathrm{amount}\times \mathrm{Time}}$

$$\begin{gathered} \mathrm{=}\frac{1000\times 100}{1000\times 8} \\ =\frac{100}{8} \\ =12.5 \end{gathered}$$

Hence, rate of interest offered by bank in simple interest is $12.5\%$.

Case $2:$ When the bank offers compound interest:

Now compound interest,

Compound Interest $\text{= P(1 +}\frac{R}{100}{)}^T-P$

Most banks calculate interests by compounding them either monthly/ quarterly/half-yearly or annually.

When amount doubles, to calculate the number of years of deposit, we use

$\frac{70}{\mathrm{Interest}\mathrm{rate}\left(\mathrm{R}\right)}=\mathrm{Time}\left(\mathrm{T}\right)$ rule.

Therefore, by using this rule, we get,

Interest rate $=\frac{70}{8}=8.75\%$

Hence, rate of interest offered by bank in compound interest is $8.75\%$.