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Equal sums of money are deposited in two different banks by ABC Enterprises, one at compound interest, compounded annually and the other at simple interest, both at 5% per annum. If after two years, the difference in the amounts comes to Rs. 200, what are the amounts deposited with each bank?
- a)Rs. 75,000
- b)Rs. 80,000
- c)Rs. 82,000
- d)Rs. 85,000
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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To find the amounts deposited with each bank, we can set up the following equation:
Compound Interest Amount - Simple Interest Amount = Rs. 200
Let's assume the amount deposited in each bank is 'P' rupees.
Calculation:
Step 1: Calculate Compound Interest (CI)
Compound Interest formula:
CI = P(1 + r/n)^(nt) - P
Where:
P = Principal amount (amount deposited)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, P is the same for both banks, r = 5% = 0.05, n = 1 (compounded annually), and t = 2 years.
CI = P(1 + 0.05/1)^(1*2) - P
CI = P(1.05)^2 - P
CI = 1.1025P - P
CI = 0.1025P
Step 2: Calculate Simple Interest (SI)
Simple Interest formula:
SI = P * r * t
In this case, P is the same for both banks, r = 5% = 0.05, and t = 2 years.
SI = P * 0.05 * 2
SI = 0.1P
Step 3: Calculate the Difference
The difference between the Compound Interest amount and the Simple Interest amount is given as Rs. 200.
CI - SI = 0.1025P - 0.1P = Rs. 200
0.0025P = Rs. 200
P = Rs. 200 / 0.0025
P = Rs. 80,000
Therefore, the amount deposited with each bank is Rs. 80,000.
Compound Interest Amount - Simple Interest Amount = Rs. 200
Let's assume the amount deposited in each bank is 'P' rupees.
Calculation:
Step 1: Calculate Compound Interest (CI)
Compound Interest formula:
CI = P(1 + r/n)^(nt) - P
Where:
P = Principal amount (amount deposited)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, P is the same for both banks, r = 5% = 0.05, n = 1 (compounded annually), and t = 2 years.
CI = P(1 + 0.05/1)^(1*2) - P
CI = P(1.05)^2 - P
CI = 1.1025P - P
CI = 0.1025P
Step 2: Calculate Simple Interest (SI)
Simple Interest formula:
SI = P * r * t
In this case, P is the same for both banks, r = 5% = 0.05, and t = 2 years.
SI = P * 0.05 * 2
SI = 0.1P
Step 3: Calculate the Difference
The difference between the Compound Interest amount and the Simple Interest amount is given as Rs. 200.
CI - SI = 0.1025P - 0.1P = Rs. 200
0.0025P = Rs. 200
P = Rs. 200 / 0.0025
P = Rs. 80,000
Therefore, the amount deposited with each bank is Rs. 80,000.
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Equal sums of money are deposited in two different banks by ABC Enterprises, one at compound interest, compounded annually and the other at simple interest, both at 5% per annum. If after two years, the difference in the amounts comes to Rs. 200, what are the amounts deposited with each bank?a)Rs. 75,000b)Rs. 80,000c)Rs. 82,000d)Rs. 85,000e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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