Question

A sum of money put loaned on compound interest, reckoned yearly, amounts to Rs.17340 in two years & to Rs.19652 in three years. Find the rate of interest & the sum.​

Answer 1

Given:

A sum of money put loaned on compound interest, reckoned yearly, amounts to Rs.17340 in two years & to Rs.19652 in three years. Find the rate of interest & the sum.​

To find:

The rate of interest & the sum.​

Solution:

We know,

$\boxed{\bold{A = P [1 + \frac{R}{100} ]^n}}$

where A = amount, P = principal, R = rate of interest and n = no. of years

Based on the formula above, we can form the following two equations using the given information in the question:

Equation 1 → $17340 = P [1 + \frac{R}{100} ]^2$

Equation 2 → $19652 = P [1 + \frac{R}{100} ]^3$

On dividing equation (2) by (1), we get

$\frac{19652}{17340} = \frac{P [1 + \frac{R}{100} ]^3}{P [1 + \frac{R}{100} ]^2}$

$\implies \frac{19652}{17340} = \frac{ [1 + \frac{R}{100} ]^3}{ [1 + \frac{R}{100} ]^2}$

$\implies \frac{19652}{17340} = [1 + \frac{R}{100} ]$

$\implies 1.1333 = [1 + \frac{R}{100} ]$

$\implies 1.1333 - 1 = \frac{R}{100}$

$\implies 0.1333 = \frac{R}{100}$

$\implies R = 0.1333 \times 100$

$\implies \bold{R = 13.33\%}$

On substituting the value of R in equation (1), we get

$17340 = P [1 + \frac{13.33}{100} ]^2$

$\implies 17340 = P [1.1333 ]^2$

$\implies P = \frac{17340}{[1.1333 ]^2}$

$\implies \bold{P = 13500.79}$

Thus,

The rate of interest is → 13.33%.

The sum of money is → Rs. 13500.79.

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