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A bank gives 12% per annum interest on an account. If the interest is compounded half-yearly, then _______ of the principal would have been earned mor
Question

A bank gives 12% per annum interest on an account. If the interest is compounded half-yearly, then _______ of the principal would have been earned more in a year as interest on the account.

A.

0.36%

B.

3.6%

C.

0.18%

D.

1.8%

Correct option is A

Given:

Annual interest rate = 12%

Compounded half-yearly

Time = 1 year

Formula Used:

Compound Amount for half-yearly compounding:

A = P(1+R/2100)2P \left(1 + \frac{R/2}{100} \right)^{2}​​

Compound Interest (CI) = A − P

Simple Interest (SI) = P×R×T100\frac{P \times R \times T}{100}​​

Difference = CI − SI

Solution:

Let Principal P = 100

Half-yearly rate = 122=6%\frac{12}{2} = 6\%​​

Compounded twice:

A = 100(1+6100)2100 \left(1 + \frac{6}{100} \right)^2​​

=100×(1.06)2= 100 \times (1.06)^2​​

=100×1.1236= 100 \times 1.1236​​

= 112.36

CI = 112.36 - 100 = 12.36

Now, 

SI = 100×12100=12100 \times \frac{12}{100} = 12​​

Extra Interest = 12.36 - 12 = 0.36

Thus, 0.36% more would be earned in a year.

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