The compound interest on a sum for two years is Rs 832 and the simple

1.	The compound interest on a sum for two years is Rs 832 and the simple interest on the same sum at the same rate for the same period is Rs 800. What is the rate of interest ? (a) 6% (b) 8%(c) 10% (d) 12%
Answer» (b) 8% Let the sum be Rs P and rate of interest per annum be R% Then, P\(\Big[\big(1+\frac{R}{100}\big)^2-1\Big]\) - \(\frac{2PR}{100}\) = Rs 832 – Rs 800 = Rs 32 \(\Rightarrow\) P\(\Big[1+\frac{2R}{100}+\frac{R^2}{10000}-1\Big]\) - \(\frac{2PR}{100}\) = 32 \(\Rightarrow\) \(\frac{PR^2}{10000}\) = 32 \(\Rightarrow\) PR x R = 320000.......(i) Also, \(\frac{2PR}{100}\) = 800 (S.I) \(\Rightarrow\) PR = 40000 ..........(ii) \(\therefore\) From (i) and (ii) 40000 × R = 320000 \(\Rightarrow\) R = 8% p.a

The compound interest on a sum for two years is Rs 832 and the simple interest on the same sum at the same rate for the same period is Rs 800. What is the rate of interest ? (a) 6% (b) 8%(c) 10% (d) 12%

Answer»

(b) 8%

Let the sum be Rs P and rate of interest per annum be R%

Then, P\(\Big[\big(1+\frac{R}{100}\big)^2-1\Big]\) - \(\frac{2PR}{100}\)

= Rs 832 – Rs 800 = Rs 32

\(\Rightarrow\) P\(\Big[1+\frac{2R}{100}+\frac{R^2}{10000}-1\Big]\) - \(\frac{2PR}{100}\) = 32

\(\Rightarrow\) \(\frac{PR^2}{10000}\) = 32 \(\Rightarrow\) PR x R = 320000.......(i)

Also, \(\frac{2PR}{100}\) = 800 (S.I) \(\Rightarrow\) PR = 40000 ..........(ii)

\(\therefore\) From (i) and (ii)

40000 × R = 320000 \(\Rightarrow\) R = 8% p.a