Compound Interest

Step 1: Compound Interest Formula.
The compound interest formula is given by: $A%20%3D%20P%20%5Cleft(%201%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%5Cright)%5E%7Bnt%7D$ where: $P%20%3D%2015000$ , $r%20%3D%208%25$ , $t%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%5C%2C%20%5Ctext%7Byears%7D$ , and $n$ is the number of compounding periods.

Step 2: Case 1 - Compounded Semi-Annually.
For semi-annual compounding, $n%20%3D%202$ . The formula becomes: $A%20%3D%2015000%20%5Cleft(%201%20%2B%20%5Cfrac%7B8%7D%7B2%20%5Ctimes%20100%7D%20%5Cright)%5E%7B2%20%5Ctimes%20%5Cfrac%7B3%7D%7B2%7D%7D%20%3D%2015000%20%5Cleft(%201%20%2B%200.04%20%5Cright)%5E%7B3%7D%20%3D%2015000%20%5Ctimes%201.04%5E3$ Calculating $1.04%5E3$ , we get: $A%20%5Capprox%2015000%20%5Ctimes%201.124864%20%3D%2016872.96$ Thus, the compound interest is: $CI_%7B%5Ctext%7Bsemi%7D%7D%20%3D%2016872.96%20-%2015000%20%3D%201872.96%20%5Capprox%201873$

Step 3: Case 2 - Compounded Annually.
For annual compounding, $n%20%3D%201$ . The formula becomes: $A%20%3D%2015000%20%5Cleft(%201%20%2B%20%5Cfrac%7B8%7D%7B100%7D%20%5Cright)%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%3D%2015000%20%5Ctimes%201.08%5E%7B1.5%7D$ Calculating $1.08%5E%7B1.5%7D$ , we get: $A%20%5Capprox%2015000%20%5Ctimes%201.121032%20%3D%2016815.48$ Thus, the compound interest is: $CI_%7B%5Ctext%7Bannual%7D%7D%20%3D%2016815.48%20-%2015000%20%3D%201815.48%20%5Capprox%201815$

Step 4: Difference in Interest.
The difference in compound interest is: $CI_%7B%5Ctext%7Bsemi%7D%7D%20-%20CI_%7B%5Ctext%7Bannual%7D%7D%20%3D%201873%20-%201815%20%3D%2058$ Thus, the difference is ₹58.

Final Answer: $%5Cboxed%7B20%7D$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Compound Interest

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs