Mr. X borrowed 8,000 from a bank on compound interest at the rate of 12% per annum for 3 years and loaned it on simple interest to Mr. Y at 15% per annum for the same period. The gain or loss of Mr. X in the transaction is
To find the gain or loss of Mr. X in this transaction, we first need to calculate the amount of interest he pays to the bank and the amount of interest he receives from Mr. Y.
Interest paid to the bank:
Principal (P) = $8,000
Rate (R) = 12% = 0.12 per annum
Time (T) = 3 years
Using the compound interest formula: I = P(1 + R)^T - P
The interest paid to the bank is: I = $8,000(1 + 0.12)^3 - $8,000
I = $8,000(1.12^3) - $8,000
I = $8,000(1.404928) - $8,000
I = $11,239.42 - $8,000
I = $3,239.42
Interest received from Mr. Y:
Principal (P) = $8,000
Rate (R) = 15% = 0.15 per annum
Time (T) = 3 years
Using the simple interest formula: I = PRT
The interest received from Mr. Y is: I = $8,000 * 0.15 * 3
I = $3600
The gain or loss of Mr. X in this transaction is the difference between the interest received and the interest paid:
Gain or Loss = Interest received - Interest paid
Gain or Loss = $3,600 - $3,239.42
Gain or Loss = $360.58
Therefore, Mr. X has a gain of $360.58 in this transaction.