Aptitude | Compound Interest | Question 2

Ram deposits Rs.2000 each on 1^st January and 1^st July of a year at the rate of 8% compound interest calculated on half-yearly basis. At the end of the year how much amount he would have?
(A) Rs.2150.50
(B) Rs.3182.40
(C) 4243.20
(D) 280.40

Answer: (C)
Explanation: We can break this problem into two parts: Rs. 1500 invested for 1 year (Jan to Dec) and Rs. 2000 invested for 6 months (Jul to Dec)
When interest is compounded Half-yearly:
Amount = P[1+ (R/2)/100 ]²ⁿ
The total amount for the investment on 1^st Jan is:
Amount1 = Rs. 2000 x [1+ (8/2)/100]^2×1
= Rs. 2000 x [1 + (4/100)]²
= Rs. 2000 x [26/25]²
The total amount for investment on 1^st july is:
Amount2 = Rs. 2000 x [1+ (8/2)/100][2 x(1/2)]
= Rs. 2000 x [1+ 4/100 ]
= Rs. 2000 x [26/25]
The total amount at the end of the year = amount1 + amount2
= 2000 x [26/25]² + 2000 x [26/25]
= 2000 x [26/25] x [(26/25) + 1]
= 2000 x 26/25 x 51/25
= 4243.20
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