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# I borrowed ₹ 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?

We have given data : P = ₹ 12,000, R = 6% p.a. and n = 2 years
So, SI for 4 months =$$\frac{P \times R \times n}{100\times 12}$$

=$$\frac{12,000\times 6 \times 2}{100}$$

=$$₹ 1440$$

Therefore we have, CI=A - P

=$$P(1+\frac{R}{100})^n$$-P

=$$12,000(1+\frac{6}{100})^2$$-12,000

=$$12,000(\frac{53}{50})^3$$-12,000

=$$12,000\times (\frac{53}{50}\times \frac{53}{50})$$-12,000

=$$12,000\times (\frac{2809}{2500})$$-12,000

=$$12,000 \times (\frac{2809}{2500}-1)$$

=$$12,000 \times (\frac{2809-2500}{1000})$$

=$$12,000 \times (\frac{309}{2500})$$

=$$\frac{7416}5 = ₹ 1483.20$$

So, the difference between the two interests = ₹ 1483.20 – ₹ 1440 = ₹ 43.20

Hence, Fabina pays more interest by ₹ 43.20.