Discussion of Question with ID = 084 under Compound-Interest

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Question

A bank offers an interest rate of 9% compounded annually. Initially I deposit Rs. 50000 in the bank under this scheme. After 1 year I again deposit Rs 50000. What is the total amount that I will get after 2 years?

A

Rs. 113905.

B

Rs. 114005.

C

Rs. 113805.

D

Rs. 114105.

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 = 9 and P = 50000 and cancelling 10000, we get 5 × 109 × 209 = Rs. 113905.


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