Question

a sum of money amount to 13230 in one year and 13891.50 in 1 and 1/2 years at C.I.,compounded semi annually .find the sum and the rate of interest per annum
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Answer 1

Let P is the sum and rate of interest per annum is r%.

Given S1 = 13230

and S2 = 13891.5

Rate of interest half-yearly = r/2 %

Now, time n1 = 2 and n2 = 3 {since rate of interest is calculated as half yearly}

Now A = P(1 + r/100)n

So, 13230 = P{1 + (r/2)/100}2

=> 13230 = P{1 + r/200}2 .................1

=> 13891.5 = P{1 + (r/2)/100}3

=> 13891.5 = P{1 + r/200}3 .............2

Now, divide equation 2 by equation 1, we get

=> 13891.5/13230 = [P{1 + r/200}3 ]/[P{1 + r/200}2 ]

=> 1 + r/200 = 13891.5/13230

=> 1 + r/200 = 1.05

=> r/200 = 1.05 - 1

=> r/200 = .05

=> r/200 = 5/100

=> r/2 = 5

=> r = 2*5

=> r = 10

So, rate of interest is 10 %

Now, from equation 1, we get

13230 = P{1 + 10/200}2

=> 13230 = P{1 + 1/20}2

=> 13230 = P{21/20}2

=> 13230 = P{(21/20)*(21/20)}

=> 13230 = 441P/400

=> P = (13230 * 400)/441

=> P = 30 * 400

=> P = 12000