A sum of money invested at compound interest amounts in 3 years to Rs

1.	A sum of money invested at compound interest amounts in 3 years to Rs 2400 and in 4 years to Rs 2520. The interest rate per annum is (a) 5% (b) 6% (c) 10% (d) 12%
Answer» (a) 5% Let the sum of money invested be Rs x and interest rate per annum = r% Then, x\(\big(1+\frac{r}{100}\big)^3\) = Rs 2400 .....(i) and x\(\big(1+\frac{r}{100}\big)^4\) = Rs 2520 ........(ii) Dividing equation (ii) by (i), we get \(\big(1+\frac{r}{100}\big)\) = \(\frac{2520}{2400}\) \(\Rightarrow\) \(\frac{r}{100}\) = \(\frac{2520-2400}{2400}\) = \(\frac{120}{2400}\) \(\Rightarrow\) r = \(\frac{1}{20}\)x 100 = 5% p.a

A sum of money invested at compound interest amounts in 3 years to Rs 2400 and in 4 years to Rs 2520. The interest rate per annum is (a) 5% (b) 6% (c) 10% (d) 12%

Answer»

(a) 5%

Let the sum of money invested be Rs x and interest rate per annum = r%

Then, x\(\big(1+\frac{r}{100}\big)^3\) = Rs 2400 .....(i)

and x\(\big(1+\frac{r}{100}\big)^4\) = Rs 2520 ........(ii)

Dividing equation (ii) by (i), we get

\(\big(1+\frac{r}{100}\big)\) = \(\frac{2520}{2400}\) \(\Rightarrow\) \(\frac{r}{100}\) = \(\frac{2520-2400}{2400}\) = \(\frac{120}{2400}\)

\(\Rightarrow\) r = \(\frac{1}{20}\)x 100 = 5% p.a