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Question 55
The simple interest on a sum at 3% p.a in 3 years is ₹315. What is the compound interest on the same sum at 4% p.a in 2 years, interest compounded yearly?
Solution
$$\frac{31500}{9}=principal$$
= $$3500\left[\frac{10816}{10000}-1\right]$$
= $$3500\times\frac{816}{10000}$$
= $$\frac{2856000}{10000}$$
= ₹285.6
The simple interest on a sum at 3% p.a in 3 years is ₹315.
$$simple\ interest\ =\frac{principal\times rate\times time}{100}$$
$$315=\frac{principal\times3\times3}{100}$$
$$31500=principal\times9$$$$\frac{31500}{9}=principal$$
principal = 3500
compound interest on the same sum at 4% p.a in 2 years, interest compounded yearly.
compound interest = $$principal\left[\left(1+\frac{rate}{100}\right)^{time}-1\right]$$
= $$3500\left[\left(1+\frac{4}{100}\right)^2-1\right]$$
= $$3500\left[\left(\frac{104}{100}\right)^2-1\right]$$= $$3500\left[\frac{10816}{10000}-1\right]$$
= $$3500\times\frac{816}{10000}$$
= $$\frac{2856000}{10000}$$
= ₹285.6
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