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Find the compound interest on Rs. 1000 at the rate of $8 %$ per annum for $112$ years when interest is compounded half yearly.

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Rs.184.86

Rs.124.86

Rs. 834.86

Rs.224.86

answer is A.

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Detailed Solution

Given,

Principal (P) = Rs 1000 Rate (R) = 8 % p .a . Time (T) = 112 years

Compound interest can be evaluated by Amount-Principal.
Also given interest is compounded half yearly.
So, rate of interest compounded half yearly

= 82 % per half year

Time will also be taken in term of years that is,

T = 32 × 2 = 3 half years

The formula to calculate the amount is given by,

A = P 1 + R 100 n ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (1)

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

A = 1000 1 + 4100 3 ⇒ A = 1000 1.04 3 ⇒ A = 1000 × 1.12486 ⇒ A = 11248.6

Therefore, the amount after 3 half years is Rs. 1124.86.
Compound interest (CI) is,

C I = A − P ⇒ C I = 1124.86 − 1000 ⇒ C I = Rs 124 .86

Therefore, the compound interest is Rs. 124.86,
Hence, the compound interest calculated is Rs. 124.86.
Therefore, option (1) is correct.

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