Question

The compound interest on a sum at 18% p.a. for 1 ½ years, compounded yearly, is ₹2 862. Find the principal.

• A. ₹10,000
• B. ₹8,000
• C. ₹2,000
• D. ₹4,000

Answer 1

Answer:

A. ₹10,000

For $(1\frac{1}{2})$ years compounded yearly:

• Interest for the first 1 year is compounded.

• For the remaining $( \frac{1}{2} )$ year, simple interest is calculated on the amount after 1 year.

Let the principal be (P).

After 1 year at (18%):

$\text{Amount} = P\left(1+\frac{18}{100}\right)=1.18P$

For the next half-year:

$\text{Interest} = 1.18P \times \frac{18}{100} \times \frac12$
$=1.18P \times 0.09$
$=0.1062P$

So total amount after $(1\frac12)$ years:

$1.18P + 0.1062P = 1.2862P$

Compound interest:

$1.2862P - P = 0.2862P$

Given:

$0.2862P = 2862$
$P = \frac{2862}{0.2862}$
$P = 10,000$

=₹10,000