The difference between simple interest and compound interest on Rs 120

1.	The difference between simple interest and compound interest on Rs 1200 for one year at 10% per annum reckoned half yearly is (a) Rs 2.50 (b) Rs 3 (c) Rs 3.75 (d) Rs 4
Answer» (b) Rs 3 P = Rs 1200, R = 10% p.a., T = 1 year \(\therefore\) S.I. = \(\frac{P\times R\times T}{100}\) = \(\frac{1200\times 10\times 1}{100}\) = Rs 120 For C.I. reckoned half yearly, P = Rs 1200, r = 5% per half year, n = 2 half year \(\therefore\) C.I = Rs \(\Big(1200\big(1+\frac{5}{100}\big)^2-1200\Big)\) = Rs\(\big(1200\times\frac{21}{20}\times\frac{21}{20}-1200\big)\) = Rs 1323- Rs 1200 = Rs 123. \(\therefore\) Required difference = Rs 123 – Rs 120 = Rs 3.

The difference between simple interest and compound interest on Rs 1200 for one year at 10% per annum reckoned half yearly is (a) Rs 2.50 (b) Rs 3 (c) Rs 3.75 (d) Rs 4

Answer»

(b) Rs 3

P = Rs 1200, R = 10% p.a., T = 1 year

\(\therefore\) S.I. = \(\frac{P\times R\times T}{100}\) = \(\frac{1200\times 10\times 1}{100}\) = Rs 120

For C.I. reckoned half yearly,

P = Rs 1200, r = 5% per half year, n = 2 half year

\(\therefore\) C.I = Rs \(\Big(1200\big(1+\frac{5}{100}\big)^2-1200\Big)\)

= Rs\(\big(1200\times\frac{21}{20}\times\frac{21}{20}-1200\big)\)

= Rs 1323- Rs 1200 = Rs 123.

\(\therefore\) Required difference = Rs 123 – Rs 120 = Rs 3.