Questions :
The compound interest on a sum at 18% p.a. for 1½ years, compounded yearly, is ₹1,431. Find the principal.
Options :
- ₹5,000
- ₹8,000
- ₹2,000
- ₹4,000
correct answer : a)
Explanation :
Let the principal be P.
For 1½ years compounded yearly:
Amount after 1 year = P × (1 + 18/100)
= 1.18P
For the remaining ½ year, simple interest is calculated on 1.18P.
Interest for ½ year = (1.18P × 18 × 0.5)/100
= 0.1062P
Total amount after 1½ years
= 1.18P + 0.1062P
= 1.2862P
Compound Interest = Amount − Principal
= 1.2862P − P
= 0.2862P
Given,
0.2862P = 1431
⇒ P = 1431 / 0.2862
⇒ P = 5000
Therefore, the principal is ₹5,000.
Hence, the correct answer is option (a) ₹5,000. The values ₹8,000, ₹2,000, and ₹4,000 do not produce a compound interest of ₹1,431 at 18% p.a. for 1½ years and are therefore incorrect.