A man invests ₹ 3072 for two years at compound interest. After one year the money amounts to ₹ 3264. Find the rate of interest and the amount due at the end of 2nd year.
Solution:
It is given that
Principal (P) = ₹ 3072
Amount (A) = ₹ 3264
Period (n) = 1 year
We know that
A/P = (1 + r/100)n
Substituting the values
3264/3072 = (1 + r/100)1
By further calculation
1 + r/100 = 17/16
r/100 = 17/16 – 1 = 1/16
By cross multiplication
r = 100 × 1/16 = 25/4 = 6 ¼
Hence, the rate of interest is 6 ¼%.
Here
Amount after 2 years = 3072 (1 + 25/ (4 × 100))2
By further calculation
= 3072 (1 + 1/16)2
So we get
= 3072 × 17/16 × 17/16
= ₹ 3468
Hence, the amount due at the end of 2 years is ₹ 3468.
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