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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.

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Solution

It is given that
Amount after one year = 13230
Amount after 112 years = 13891.50
So the difference = 13891.5013230=661.50
Here 661.50 is the interest on 13230 for 12 years
We know that
Rate = (661.50×100×2)/(13230×1)
Multiplying and dividing by 100
=(66150×100×2)/(13230×1×100)
=10% p.a.
Here
A = P(1+r/100)n
Substituting the values
13891.50=P×21/20×21/20×21/20
So we get
P=13891.50×20/21×20/21×20/21
P= 12000

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