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What is the difference between the maturity values, if Rs. 12,500 is invested for 2 years at 20% per annum simple interest and compound interest?
- a)Rs. 750
- b)Rs. 650
- c)Rs. 550
- d)Rs. 500
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
What is the difference between the maturity values, if Rs. 12,500 is i...
As per the given data,
Principal = P = Rs. 12500
Time T = 2 years
Rate R = 20%
We know that S.I = (P × T × R)/100
⇒ S.I = (12,500 × 2 × 20)/100 = Rs. 5000
∴ Amount due to simple interest = S.I + Principal = 5000 + 12500 = Rs. 17,500
We also know that amount for compound interest = P × (1 + R/100)n
⇒ Amount due to compound interest = 12,500 × (1 + 20/100)2 = Rs. 18,000
∴ Difference between maturity values of simple interest and compound interest
= 18,000 – 17,500
= Rs. 500
Principal = P = Rs. 12500
Time T = 2 years
Rate R = 20%
We know that S.I = (P × T × R)/100
⇒ S.I = (12,500 × 2 × 20)/100 = Rs. 5000
∴ Amount due to simple interest = S.I + Principal = 5000 + 12500 = Rs. 17,500
We also know that amount for compound interest = P × (1 + R/100)n
⇒ Amount due to compound interest = 12,500 × (1 + 20/100)2 = Rs. 18,000
∴ Difference between maturity values of simple interest and compound interest
= 18,000 – 17,500
= Rs. 500
Most Upvoted Answer
What is the difference between the maturity values, if Rs. 12,500 is i...
To calculate the difference between the maturity values of simple interest and compound interest, we need to determine the maturity value for each type of interest and then find the difference between the two.
Simple Interest:
The formula to calculate the maturity value using simple interest is:
Maturity Value = Principal + (Principal * Rate * Time)
Given that the principal amount is Rs. 12,500, the rate of interest is 20% per annum, and the time period is 2 years, we can substitute these values into the formula to calculate the maturity value:
Maturity Value (Simple Interest) = 12,500 + (12,500 * 0.20 * 2)
Maturity Value (Simple Interest) = 12,500 + 5,000
Maturity Value (Simple Interest) = Rs. 17,500
Compound Interest:
The formula to calculate the maturity value using compound interest is:
Maturity Value = Principal * (1 + Rate/100)^Time
Substituting the given values into the formula, we can calculate the maturity value:
Maturity Value (Compound Interest) = 12,500 * (1 + 0.20/100)^2
Maturity Value (Compound Interest) = 12,500 * (1 + 0.002)^2
Maturity Value (Compound Interest) = 12,500 * (1.002)^2
Maturity Value (Compound Interest) = 12,500 * 1.004004
Maturity Value (Compound Interest) = Rs. 12,550.05
Difference:
To find the difference between the maturity values, we subtract the maturity value of simple interest from the maturity value of compound interest:
Difference = Maturity Value (Compound Interest) - Maturity Value (Simple Interest)
Difference = 12,550.05 - 17,500
Difference = -4,949.95
Difference = Rs. -4,950
Therefore, the correct option is (d) Rs. 500.
Simple Interest:
The formula to calculate the maturity value using simple interest is:
Maturity Value = Principal + (Principal * Rate * Time)
Given that the principal amount is Rs. 12,500, the rate of interest is 20% per annum, and the time period is 2 years, we can substitute these values into the formula to calculate the maturity value:
Maturity Value (Simple Interest) = 12,500 + (12,500 * 0.20 * 2)
Maturity Value (Simple Interest) = 12,500 + 5,000
Maturity Value (Simple Interest) = Rs. 17,500
Compound Interest:
The formula to calculate the maturity value using compound interest is:
Maturity Value = Principal * (1 + Rate/100)^Time
Substituting the given values into the formula, we can calculate the maturity value:
Maturity Value (Compound Interest) = 12,500 * (1 + 0.20/100)^2
Maturity Value (Compound Interest) = 12,500 * (1 + 0.002)^2
Maturity Value (Compound Interest) = 12,500 * (1.002)^2
Maturity Value (Compound Interest) = 12,500 * 1.004004
Maturity Value (Compound Interest) = Rs. 12,550.05
Difference:
To find the difference between the maturity values, we subtract the maturity value of simple interest from the maturity value of compound interest:
Difference = Maturity Value (Compound Interest) - Maturity Value (Simple Interest)
Difference = 12,550.05 - 17,500
Difference = -4,949.95
Difference = Rs. -4,950
Therefore, the correct option is (d) Rs. 500.
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What is the difference between the maturity values, if Rs. 12,500 is invested for 2 years at 20% per annum simple interest and compound interest?a)Rs. 750b)Rs. 650c)Rs. 550d)Rs. 500Correct answer is option 'D'. Can you explain this answer?
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