A bank offers 5% comp

Question

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

Options:

A . Rs. 120

B . Rs. 121

C . Rs. 123

D . Rs. 122

Answer: Option B

Answer : Option B

Explanation :

Amount after 1 year on Rs. 1600 (deposited on 1st Jan) at 5% when interest calculated half-yearly
$MF#%= \text{P}\left(1 + \dfrac{\text{(R/2)}}{100}\right)^\text{2T}
= 1600\left(1 + \dfrac{\text{(5/2)}}{100}\right)^{2 \times 1}
= 1600\left(1 + \dfrac{1}{40}\right)^2$MF#%
Amount after 1/2 year on Rs. 1600 (deposited on 1st Jul) at 5% when interest calculated half-yearly
$MF#%= \text{P}\left(1 + \dfrac{\text{(R/2)}}{100}\right)^\text{2T} = 1600\left(1 + \dfrac{\text{(5/2)}}{100}\right)^{2 \times \frac{1}{2}} = 1600\left(1 + \dfrac{1}{40}\right)$MF#%
Total Amount after 1 year
$MF#%=1600\left(1 + \dfrac{1}{40}\right)^2 + 1600\left(1 + \dfrac{1}{40}\right)
= 1600\left( \dfrac{41}{40}\right)^2 + 1600\left(\dfrac{41}{40}\right)
= 1600\left( \dfrac{41}{40}\right)\left[1 + \dfrac{41}{40}\right]\\\\ = 1600\left( \dfrac{41}{40}\right)\left( \dfrac{81}{40}\right) = 41 \times 81 = \text{Rs. }3321$MF#%
Compound Interest = Rs.3321 - Rs.3200 = Rs.121

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