A certain sum amounts to ₹ 5292 in 2 years and to ₹ 5556.60 in 3 years at compound interest. Find the rate and the sum.
Solution:
It is given that
Amount after 2 years = ₹ 5292
Amount after 3 years = ₹ 5556.60
So the difference = 5556.60 – 5292 = ₹ 264.60
Here ₹ 264.60 is the interest on ₹ 5292 for one year
We know that
Rate % = (SI × 100)/ (P × t)
Substituting the values
= (264.60 × 100)/ (5292 × 1)
Multiply and divide by 100
= (26460 × 100)/ (100 × 5292)
= 5%
Here
A = P (1 + r/100)n
Substituting the values
5292 = P (1 + 5/100)2
By further calculation
P = 5292 ÷ (1 + 5/100)2
So we get
P = 5292 ÷ (21/20)2
P = 5292 × 21/20 × 21/20
P = ₹ 4800
Hence, the rate is 5% and the sum is ₹ 4800.
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