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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