Question 53

The compound interest on a certain sum at 10% p.a. for $$2\frac{1}{3}$$ years is ₹1,201.60, interest compounded yearly. The sum is:

Solution

r = 10%

Time(t) = $$2\frac{1}{3} = 7/3 years$$

Compound interest = 1201.6

Compound interest = p(1 + $$\frac{r}{100})^t - p$$

1201.6 = p(1 + $$\frac{10}{100})^{7/3} - p$$

1201.6 = p(1 + $$\frac{10}{100})^{(2 + 1/3)} - p$$

1201.6 = $$p\times (110/100) \times (110/100) \times (110/100)^{1/3} - p$$

1201.6 = 1.25p - p

p = 1201.6/0.25 = 4806.4 $$\approx$$ Rs.4800

$$\therefore$$ The sum is Rs.4800.

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