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# 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?

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?

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For Fabina,

Principal,P =Rs 12500

Simple interest Rate,R = 12% p.a.

Time period,n = 3 years.

$\therefore$ Simple Interest, SI at 12% for 3 years = $3\times\frac{12500\times12}{100}$ = Rs 4500

Principal,P =Rs 12500

Compound interest Rate,R = 10% p.a.

Time period,n = 3 years.

We know, Amount when interest is compounded annually,

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

$A=12500(1+\frac{10}{100})^3 = Rs 16637.50$

$\therefore Compound \:\:Interest, CI = A - P = Rs\: (16637.50 - 12500) = Rs \:4137.50$

$\therefore$ Fabina pays more interest and Rs (4500 - 4137.50) = Rs 362.50 more.

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