Question

Find the rate of interest if the compound interest on Rs.50,000 for 2years compounded half-yearly is Rs.23,205.​

Answer 1

Answer:

The rate of interest is 20 %.

Step-by-step-explanation:

We have given that,

• Principal ( P ) = Rs 50000
• Time ( T ) = 2 years
• Number of times interest compounded ( N ) = 2
• Compound interest = Rs 23205

We have to find the rate of interest ( R ).

As the interest is compounded half yearly, rate of interest is R / 2.

We know that,

Amount = Principal + Compound interest

⇒ Amount = Rs 50000 + Rs 23205

⇒ Amount = Rs 73205

Now,

Amount = Principal [ 1 + ( Rate / 100 ) ]ᴺᵀ

⇒ 73205 = P [ 1 + ( R / 2 ) / 100 ]²*²

⇒ 73205 = 50000 [ 1 + ( R / 200 ) ]⁴

⇒ 73205 / 50000 = [ ( 200 + R ) / 200 ]⁴

⇒ 1.4641 = [ ( 200 + R ) / 200 ]⁴

Taking fourth root on both sides,

⇒ ∜1.4641 = ( 200 + R ) / 200

⇒ 1.1 = ( 200 + R ) / 200

⇒ 1.1 * 200 = 200 + R

⇒ 220 = R + 200

⇒ R = 220 - 200

⇒ R = 20 %

∴ The rate of interest is 20 %.