What annual installment will discharge a debt of ₹26,160 due in 4 years at 6% simple interest p.a.?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. ₹6,000.
The formula for the Present Value (P) of an annuity (A) for n years at a rate of interest r% per annum is:
P = A × (1 + (r × (n - 1))/2) × n
Where:
P = the total debt, A = the annual installment, r = the interest rate, and n = the number of years
Now,
⇒ 26160 = A × (1 + (0.06 × (4 - 1))/2) × 4
⇒ 26160 = A × (1 + (0.06 × 3)/2) × 4
⇒ 26160 = A × (1 + (0.18)/2) × 4
⇒ 26160 = A × (1 + 0.09) × 4
⇒ 26160 = A × 1.09 × 4
⇒ 26160 = A × 4.36
⇒ A = Rs.6000
The required annual installment to discharge the debt of ₹26,160 in 4 years at 6% simple interest per annum is ₹6,000.