The difference between compound interest and simple interest on a sum

1.	The difference between compound interest and simple interest on a sum for 2 years at 8% p.a. is Rs 768. The sum is (a) Rs 100000 (b) Rs 110000 (c) Rs 120000 (d) Rs 170000
Answer» (c) Rs 120000 Let the sum be Rs 100. Then, S.I = Rs\(\frac{100\times2\times8}{100}\) = Rs 16 C.I = Rs 100\(\Big[\big(1+\frac{8}{100}\big)^2-1\Big]\) = Rs 100\(\Big[\big(\frac{27}{25}\big)^2-1\Big]\) = Rs 100 x \(\Big[\frac{729-625}{625}\Big]\) = Rs\(\big(\frac{100\times104}{625}\big)\) = Rs 16.64 \(\therefore\) Difference = Re 0.64 If the difference between C.I. and S.I. is Re 0.64, Sum = Rs 100 If the difference is Rs 768, sum =Rs \(\big(\frac{100}{0.64}\times768\big)\) = Rs 120000.

The difference between compound interest and simple interest on a sum for 2 years at 8% p.a. is Rs 768. The sum is (a) Rs 100000 (b) Rs 110000 (c) Rs 120000 (d) Rs 170000

Answer»

(c) Rs 120000

Let the sum be Rs 100. Then,

S.I = Rs\(\frac{100\times2\times8}{100}\) = Rs 16

C.I = Rs 100\(\Big[\big(1+\frac{8}{100}\big)^2-1\Big]\)

= Rs 100\(\Big[\big(\frac{27}{25}\big)^2-1\Big]\) = Rs 100 x \(\Big[\frac{729-625}{625}\Big]\)

= Rs\(\big(\frac{100\times104}{625}\big)\) = Rs 16.64

\(\therefore\) Difference = Re 0.64 If the difference between C.I. and S.I. is Re 0.64, Sum = Rs 100

If the difference is Rs 768, sum =Rs \(\big(\frac{100}{0.64}\times768\big)\)

= Rs 120000.