What annual installment will discharge a debt of $\large\bf{₹}$ $1092$ due in $3$ years at $12\%$ Simple Interest?

Question

Question : What annual installment will discharge a debt of $\large\bf{₹}$$1092$ due in $3$ years at $12\%$ Simple Interest?

Options
a. $\large\bf{₹}$$300$
b. $\large\bf{₹}$$225$
c. $\large\bf{₹}$$400$
d. $\large\bf{₹}$$325$

My Answer : $\large\bf{₹}$$495.04$

Claimed Answer : $\large\bf{₹}$$325$

Doubt : But If the instalment is $\large\bf{₹}$$325$ then in $3$ years we pay total of $\large\bf{₹}$$975$, which is less than the disbursed loan amount of $\large\bf{₹}$$1092$. So, my question is how are we getting $\large\bf{₹}$$325$? What's the approach? Is $\large\bf{₹}$$1092$ the Principal Amount or it's the Principal Amount + Interest?

Answer 1

You have a debt which has a value of $1092$ in three years. You can say that this value is the future value of the debt.

You pay immediately an installment of $x$. This payment has to be compounded two years to get the value at the beginning of the third year. The factor is $1.24 (=1+0.12\cdot 2)$. The next (second) year you pay the next installment $x$. This installment has to be compounded by $1.12$. At the third year you just pay $x$. No compunding is needed for this payment. Therefore the equation is

$$x\cdot 1.24+x\cdot 1.12+x=1092$$