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

Question

Question

This question was previously asked in

SSC GD Constable 2025 Official Paper (Held On: 06 Feb, 2025 Shift 1)

Answer 1

Formula Used:

A = P × (1 + R/100)ⁿ

Calculation:

Let P = x

Since interest is compounded every 10 months, number of compounding periods in 2.5 years = (30 months / 10 months) = 3

Effective rate for 10 months = 12 × (10 / 12) = 10%

So,

A = x × (1 + 10/100)³

54571 = x × (110/100)³

54571 = x × (1331 / 1000)

x = 54571 × (1000 / 1331)

x = 41000

The correct value of x is ₹41000

Shortcut Trick

10% = 1/10

p : A = 10 : 11

Repeated 3 times:

10 : 11

_________

1000 : 1331

According to the question:

1331 unit = 54571

1 unit = 54571 / 1331 = 41

Then principal = 1000 unit = 41000