What annual installment will discharge a debt of Rs. 4600 due in 4 years at 10% p.a. simple interest?

Correct option is A

Ans. (a)
Sol.
Let the annual installment = Rs. x
Debt = Rs. 4600
Time = 4 years
Rate = 10% p.a. (Simple Interest)
Since payments are made in equal annual installments, we consider each installment earning simple interest from the time it's paid till the end of 4 years.
So, the present worth of each installment paid yearly (with interest till the end of 4 years) must equal Rs. 4600.
We'll calculate the present worth of each installment (i.e., its future value at the end of 4 years), then add them up and equate to Rs. 4600.
Using present worth formula with simple interest:
Present Worth = Installment × [1 + (r × t)/100]
Installments are paid at the end of each year, so they’ll have different durations of interest till the 4th year:
1st installment (paid at end of 1st year) → interest for 3 years
2nd installment → interest for 2 years
3rd installment → interest for 1 year
4th installment → no interest
So,
Total amount =
x(1 + 10×3/100) + x(1 + 10×2/100) + x(1 + 10×1/100) + x
= x(1 + 0.3) + x(1 + 0.2) + x(1 + 0.1) + x
= x(1.3 + 1.2 + 1.1 + 1)
= x × 4.6
Now,
x × 4.6 = 4600
⇒ x = 4600 / 4.6 = Rs. 1000