A sum of money was lent for 2 years at 20% compounded annually. If the interest is payable half-yearly instead of yearly, then the interest is Rs. 482 more. Find the sum.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

Rs. 20000

Rs. 20072

Rs. 22700

Rs. 29100

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given,

Rate (R) = 20 ​ ​ % ​ ​ p .a Time (T) = 2 years

Let P be the principal.
The amount on compounded half yearly is Rs 482 more than the amount compounded annually for the given rate of interest and duration.
The formula to calculate the amount is given by

A = P 1 + R 100 t

The amount when compounded annually is,

A = P 1 + 20100 2 ⇒ A = P 1.2 2 ⇒ A = 1.44 P ..... (1)

The amount when compounded half-yearly,
We know that 2 years = 4 half year

A 2 = P 1 + 20200 4 ⇒ A 2 = P 1.1 4 ⇒ A 2 = 1.4641 P ..... (2)

We know CI = Amount - Principal
According to given condition,

482 = (1.4641 P − P) − (1.44 P − P) (0 .4641 − 0.44) P = 482 P = Rs 482 0.0241 P = R s 20000

Hence, the sum is Rs. 20000
Hence, the correct option is 1.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE