What will be the annual installment (in ₹) to repay a loan of ₹9,429 payable in three years at 12.25% annual simple interest rate? [Note: The installments will be paid at the end of the first year, second year and third year.]

Let the annual installment be ₹$x$.

Since installments are paid at the end of each year:

1st installment earns interest for $2$ years

2nd installment earns interest for $1$ year

3rd installment earns no interest

Total amount after 3 years = ₹$9429$

Using simple interest:

First installment value after $2$ years:

$= x\left(1+\frac{12.25 \times 2}{100}\right)$

$= x(1+0.245)$

$= 1.245x$

Second installment value after $1$ year:

$= x\left(1+\frac{12.25}{100}\right)$

$= 1.1225x$

Third installment value:

$= x$

So,

$1.245x + 1.1225x + x = 9429$

$3.3675x = 9429$

$x = \frac{9429}{3.3675}$

$x = 2800$