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Question

Fabina borrows Rs. 12500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same period at 10% per annum, compounded annually. Who pays more interest and by how much?


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Solution

Step 1: Calculate the interest, that Fabina pays :

Principle of Fabina, P=12500 Rupees.

Rate of simple interest, r1=12%=12100=0.12.

Time period, t=3 years.

Simple interest, IS=Pr1t.

IS=12500×0.12×3IS=4500

Thus, the amount of the interest, that Fabina pays is 4500 Rupees.

Step 2: Calculate the interest, that Radha pays

Principle of Radha, P=12500 Rupees.

Rate of compound interest, r2=10%=10100=0.1.

Time period, t=3 years.

As the interest is compounded annually, thus the number of periods in one year, n=1.

Compound interest, IC=P1+r2nnt-1.

IC=12500×1+0.111×3-1IC=12500×1.13-1IC=12500×1.331-1IC=12500×0.331IC=4137.5

Thus, the amount of the interest, that Radha pays is 4137.5 Rupees.

Step 3: Compare the amount of interest

Fabina pays 4500 Rupees as interest and Radha pays 4137.5 Rupees as interest.

Hence, Fabina pays more amount as interest.

The extra amount is 4500-4137.5=362.5 Rupees.

Therefore, Fabina pays 362.5 Rupees more than Radha.


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