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# 3. Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?

We have given data for Fabina as: P = ₹ 12,500, R = 12% p.a. and n = 3 years
So, SI for 4 months =$$\frac{P \times R \times n}{100\times 12}$$

=$$\frac{12,500\times 12 \times 3}{100}$$

=$$₹ 4500$$

Therefore we have, CI=A - P

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

=$$12,500(1+\frac{10}{100})^3$$-12,500

=$$12,500(\frac{11}{10})^3$$-12,500

=$$12,500\times (\frac{10}{100}\times \frac{10}{100}\times \frac{10}{100})$$-12,500

=$$12,500\times (\frac{1331}{1000})$$-12,500

=$$12,500 \times (\frac{1331}{1000}-1)$$

=$$12,500 \times (\frac{1331-1000}{1000})$$

=$$12,500 \times (\frac{331}{1000})$$

=$$12.5\times 331 = ₹ 4137.50$$

So, the difference between the two interests = ₹ 4500 – ₹ 4137.50 = ₹ 362.50

Hence, Fabina pays more interest by ₹ 362.50.