Question : A borrows an amount of INR 3,600 from B at a rate of 20% simple interest for 2 years and lends 75% of this amount to C at 20% compound interest for 2 years. A uses the remaining amount for his purpose. Find the total loss incurred by A.
Option 1: INR 928
Option 2: INR 852
Option 3: INR 1,152
Option 4: INR 1,024
Correct Answer: INR 1,152
Solution :
Given,
Principal borrowed by A from B = INR 3,600
Rate of interest charged by B on loan = 20% per year (simple interest)
Time for which A borrowed from B = 2 years
A lent 75% of the borrowed amount to C at a rate of 20% per year (compound interest) for 2 years
We know,
Simple Interest (SI) = $\frac{P × R × T}{100}$
Compound Interest (CI) = $P × [ (1 + \frac{R}{100})^T- 1 ]$
Total interest = CI - SI
Where,
P = principal amount, R = rate of interest per annum, and T = time in years
Interest paid by A = Simple interest on loan from B = $\frac{P × R × T}{100}$
= $\frac{3600 × 20 × 2}{100}$
= IINR 1,440
Amount lent to C = 75% of INR 3,600 = INR 2,700
Interest received by A = Compound interest on the amount lent to C
= $P × [ (1 + \frac{R}{100})^T- 1 ]$
= $2700 × [ (1 + \frac{20}{100})^2 - 1 ]$
= $2700 × \frac{11}{25}$
= INR 1188
Total loss incurred By A = 1440 - 1188 + amount for his Purpose.
= 1440 - 1188 + 25% of 3600
= 1440 - 1188 + 900
= INR 1152
Hence, the correct answer is INR 1,152.
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