The difference between the simple and compound interest on a certain o...
Calculation of Simple Interest and Compound Interest
The first step in solving this problem is to calculate the simple interest and compound interest for the initial sum of money.
Simple Interest
The formula for simple interest is: SI = (P * R * T) / 100
Where, P = Principal amount, R = Rate of interest, T = Time period
In this case, P = sum of money, R = 5% p.a, and T = 3 years. Therefore, the simple interest can be calculated as:
SI = (P * R * T) / 100
SI = (P * 5 * 3) / 100
SI = 0.15P
Compound Interest
The formula for compound interest is: CI = P * (1 + R/100)^T - P
Where, P = Principal amount, R = Rate of interest, T = Time period
In this case, P = sum of money, R = 5% p.a, and T = 3 years. Therefore, the compound interest can be calculated as:
CI = P * (1 + R/100)^T - P
CI = P * (1 + 0.05)^3 - P
CI = P * 1.157625 - P
CI = 0.157625P
Difference between Simple Interest and Compound Interest
The difference between simple interest and compound interest for 3 years can be calculated as:
CI - SI = 0.157625P - 0.15P
CI - SI = 0.007625P
Given that the difference is ` 228.75, we can solve for P as:
0.007625P = 228.75
P = 30000
Compound Interest for 2 years
Now that we know the initial sum of money is ` 30000, we can calculate the compound interest for 2 years at 5% p.a as:
CI = P * (1 + R/100)^T - P
CI = 30000 * (1 + 0.05)^2 - 30000
CI = 32775
Therefore, the compound interest on the sum of ` 30000 for 2 years at 5% per annum is ` 3275. Hence, the correct option is (c) ` 3275.
The difference between the simple and compound interest on a certain o...
3075 will be right answer
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