A sum of money amounts to ₹ 13230 in one year and to ₹ 13891.50 in 1 ½ years at compound interest, compounded semi-annually. Find the sum and the rate of interest per annum.
Solution:
It is given that
Amount after one year = ₹ 13230
Amount after 1 ½ years = ₹ 13891.50
So the difference = 13891.50 – 13230 = ₹ 661.50
Here ₹ 661.50 is the interest on ₹ 13230 for ½ 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 (1 + 5/100)3
By further calculation
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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