Loan Instalment Calculation

The problem asks for the amount of each equal yearly instalment for a loan repaid with compound interest. Let the principal amount be P, the annual interest rate be R%, and the amount of each instalment be $x$. The loan is paid back in three equal annual instalments.

Problem Setup

• Principal (P) = ₹3,310
• Interest Rate (R) = 10% per annum
• Number of instalments (n) = 3
• Instalment amount = $x

Calculating Instalment Amount

The sum of the present values of all instalments must equal the principal borrowed. The formula relating principal, instalment, interest rate, and number of periods is:

$P = \frac{x}{(1 + R/100)^1} + \frac{x}{(1 + R/100)^2} + \frac{x}{(1 + R/100)^3}$

Substitute the given values: P = 3310 and R = 10.

$3310 = \frac{x}{(1 + 10/100)^1} + \frac{x}{(1 + 10/100)^2} + \frac{x}{(1 + 10/100)^3}$

$3310 = \frac{x}{(1.1)^1} + \frac{x}{(1.1)^2} + \frac{x}{(1.1)^3}$

$3310 = x \left( \frac{1}{1.1} + \frac{1}{1.21} + \frac{1}{1.331} \right)$

To simplify the terms in the parenthesis, find a common denominator, which is $1.331$.

$3310 = x \left( \frac{1 \times 1.21}{1.331} + \frac{1 \times 1.1}{1.331} + \frac{1}{1.331} \right)$

$3310 = x \left( \frac{1.21 + 1.10 + 1}{1.331} \right)$

$3310 = x \left( \frac{3.31}{1.331} \right)$

Now, solve for $x$:

$x = 3310 \times \frac{1.331}{3.31}$

$x = \frac{3310}{3.31} \times 1.331$

Since $3310 / 3.31 = 1000$,

$x = 1000 \times 1.331$

$x = 1331$

Therefore, the amount of each instalment is ₹1,331.