Question

A sum of ₹x amounts to ₹54571 in 2 1/2 years at 12% p.a., interest compounded after every 10 months. What is the value of x?

• A. 41000
• B. 39000
• C. 42000
• D. 40000

Answer 1

Answer:

A. 41000

Time = $(2 \tfrac{1}{2}) years = 30 months$

Compounded every 10 months ⇒ number of periods:
$\frac{30}{10} = 3$

So:

• Amount (A = 54571)

• Rate = 12% per year ⇒ for 10 months:
  
  $\text{rate per period} = 12\% \times \frac{10}{12} = 10\%$
  

  Compound Interest formula:

$A = P(1 + r)^n$
$54571 = x(1.1)^3$
$(1.1)^3 = 1.331$

So:
$x = \frac{54571}{1.331} = 41000$

Final Answer: ₹41,000