Question

# A sum of money amounts to 13230 in one year and to 13891.50 in 1.5 years at compound interest, compounded semi-annually . Find the sum and the rate of interest p.a.

Solution

## It is given that Amount after one year = 13230Amount after $$1 \dfrac{1}{2}$$ years = 13891.50 So the difference = $$13891.50 - 13230 = 661.50$$Here 661.50 is the interest on 13230 for $$\dfrac{1}{2}$$ years We know that Rate = $$(661.50 \times 100 \times 2)/ (13230 \times 1)$$Multiplying and dividing by 100=$$(66150 \times 100 \times 2)/(13230 \times 1 \times 100)$$=10% p.a.Here A = $$P(1 + r/100)^{n}$$Substituting the values $$13891.50 = P \times 21/20 \times 21/20 \times 21/20$$So we get $$P= 13891.50 \times 20/21 \times 20/21 \times 20/21$$P= 12000Mathematics

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