Question

In how many years does a sum of Rs.5000 yield a simple interest of Rs. 16500 at 15% pa

Answer 1

Given :

Principle : ₹5000

Simple interest : ₹16500

Rate of interest : 15%

To find :

The time taken to return the amount back.

Solution :

To find the time, we use the formula of simple interest.

Time :

$\sf \dashrightarrow Simple \: Interest = \dfrac{P \times R \times T}{100}$

$\sf \dashrightarrow 16500 = \dfrac{5000 \times 15 \times T}{100}$

$\sf \dashrightarrow 16500 = \dfrac{75000 \times T}{100}$

$\sf \dashrightarrow T = \dfrac{16500 \times 100}{75000}$

$\sf \dashrightarrow T = \dfrac{33 \times 2}{3}$

$\sf \dashrightarrow T = \dfrac{66}{3}$

$\sf \dashrightarrow T = 22$

Hence, the time taken to return the money back is 22 years.

$\:$

Verification

$\sf \dashrightarrow Simple \: Interest = \dfrac{P \times R \times T}{100}$

$\sf \dashrightarrow 16500 = \dfrac{5000 \times 15 \times 22}{100}$

$\sf \dashrightarrow 16500 = \dfrac{75000 \times 22}{100}$

$\sf \dashrightarrow 16500 = \dfrac{1650000}{100}$

$\sf \dashrightarrow 16500 = 16500$

$\sf \dashrightarrow LHS = RHS$