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Find the compound interest on Rs. 160000 for one year at the rate of $20 %$ per annum, if the interest is compounded quarterly.

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Rs.34481

Rs.62531

Rs.16281

Rs.62481

answer is A.

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Detailed Solution

Given,

Principal (P) = Rs 160000 Rate (R) = 20 % p .a . Time (T) = 1 year

Also given interest is compounded quarterly Rate of interest compounded quarterly

= 204 % per quarter year

Time (T) will also be taken quarterly that is

T = 4

quarters
The formula to calculate the amount is given by

A = P 1 + R 100 n ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (1)

Compound interest can be evaluated by Amount-Principal; where

A =

Amount,

P =

Principal,

R =

Rate,

n =

Time
Substitute the given value in equation (1) and solve for amount A,

⇒ 16000 1 + 20400 4 ⇒ 16000 1.05 4 ⇒ 19448.1

Therefore, the amount 4 quarters (1 year) is Rs 194481
Compound interest (CI),

C I = A − P ⇒ C I = 194481-160000 ⇒ C I = Rs 34481

Therefore, The Compound interest is Rs 34481
Hence, the correct option is 1.

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