The simple interest on a certain sum for 3 years is ₹ 1080 and the compound interest on the same sum at the same rate for 2 years is ₹ 741.60. Find:
(i) the rate of interest
(ii) the principal.
Solution:
It is given that
SI for 3 years = ₹ 1080
SI for 2 years = (1080 × 2)/ 3 = ₹ 720
CI for 2 years = ₹ 741.60
So the difference = 741.60 – 720 = ₹ 21.60
Here ₹ 21.60 is the SI on 720/2 = ₹ 360 for one year
(i) We know that
Rate = (SI × 100)/ (P × t)
Substituting the values
= (21.60 × 100)/ (360 × 1)
Multiply and divide by 100
= (2160 × 100)/ (100 × 360 × 1)
= 6%
(ii) ₹ 1080 is SI for 3 years at the rate of 6% p.a.
So the principal = (SI × 100)/ (r × t)
Substituting the values
= (1080 × 100)/ (6 × 3)
= ₹ 6000
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