Discussion of Question with ID = 074 under Compound-Interest

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Question

An interest rate of 4% compounded half-annually is offered by a bank. An account holder deposits Rs. 10000 in the bank under this scheme. After six months he again deposits Rs 10000. What is the total amount that he will get after 1 year?

A

Rs. 20604.

B

Rs. 21316.

C

Rs. 21116.

D

Rs. 21416.

Soln.
Ans: a

Let P, A, r and n have their usual meanings. For the first deposit n = 2, and for the second deposit n = 1. So total amount is P × $((1 + r/100)^2 + (1 + r/100))$ = $P/10000$ × $((100 + r)^2 + 100(100 + r))$ = $P/10000 × (100 + r)$ × $(100 + r + 100)$ which equals ${P × (100 + r) × (200 + r)}/10000.$ Putting r = 2 and P = 10000 and cancelling 10000, we get 1 × 102 × 202 = Rs. 20604. Please note that the rate of interest will be 1/2 because the compounding is half yearly.


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