Question

lArham lent Rs 3,000 to Ashok for 2 years at 6% p.a. simple interest. How much would Ashok gain if he lends the same amount for the same period on compound interest (compound half yearly)

Answer 1

$P \: = \: 3000 \\ \\ Time \: = \: 2 \: years \\ \\ Rate \: of \: intrest \: = \: 6\% \\ \\ simple \: intrest \: paid \: by \: ashok \: to \: arham \: = \: \frac{P \times R \times T}{100} \\ \\ \frac{300 \times 6 \times 2}{100} =₹ 360 \\ \\ amount \: returned \: by \: ashok \: to \: arham \: = \: 3000 + 360 = ₹3360 \\ \\ compound \: intrest \: received \: by \: ashok \: = \: \\ \\ P( { \frac{1 + r}{100} )}^{n} \: - 1 \\ \\ \\ 3000 \times ( { \frac{1 + 6}{100} )}^{2} - 1 \\ \\ 3000( {1.06}^{2} ) - 1 \\ \\ 3000 \times (1.1236 - 1) \\ \\ 3370.8 \\ \\ \therefore \: amount \: received \: by \: ashok \: = \: 3370.80 - 3360.00 \\ \\ = ₹10.80$