The simple interest on a certain sum at the end of three years at 5%p.a. is ₹1,200. The compound interest on the same sum for the same period at the same rate is (interest compounded yearly):
Rate(r) = 5%
Time(t) = 3
Interest = 1200
Principle = p
Interest = $$\frac{prt}{100}$$
1200 = $$\frac{p \times 5 \times 3}{100}$$
p = Rs. 8000
Compound interest = $$p(1 + \frac{r}{100})^t - p $$
= $$8000(1 + \frac{5}{100}) - 8000$$
= $$8000 \times \frac{105}{100}\times \frac{105}{100} \times \frac{105}{100} - 8000
= 2083725 - 8000
Compound interest = 9261 - 8000 = Rs. 1261
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