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A person invests Rs. 500 at the end of each year with a bank which pays interest at 10% p.a. C.I. annually. The amount standing to his credit one year after he has made his yearly investment for the 12th time is.
- a)Rs. 11761.20
- b)Rs. 10000
- c)Rs. 12000
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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A person invests Rs. 500 at the end of each year with a bank which pay...
Given:
- Principal amount (P) = Rs. 500
- Rate of interest (R) = 10% p.a.
- Compound interest is calculated annually
To find:
The amount standing to his credit one year after he has made his yearly investment for the 12th time.
Solution:
1. Calculation of Compound Interest (CI) for each year:
Since the interest is compounded annually, we can use the formula:
Amount (A) = P(1 + R/100)^n
Where,
P = Principal amount
R = Rate of interest
n = Number of years
To find the compound interest for each year, we can subtract the principal amount from the total amount.
Compound Interest (CI) = A - P
2. Calculation of the total amount after 12 years:
Since the person invests Rs. 500 at the end of each year for 12 years, the total amount can be calculated by adding the principal amount and the compound interest for each year.
Total Amount after 12 years = (Principal amount + Compound Interest for Year 1) + (Principal amount + Compound Interest for Year 2) + ... + (Principal amount + Compound Interest for Year 12)
3. Calculation:
Let's calculate the compound interest and the total amount after 12 years.
Year 1:
A = P(1 + R/100)^n
A = 500(1 + 10/100)^1
A = 500(1 + 0.1)^1
A = 500(1.1)
A = 550
CI1 = A - P
CI1 = 550 - 500
CI1 = 50
Year 2:
A = P(1 + R/100)^n
A = 500(1 + 10/100)^2
A = 500(1 + 0.1)^2
A = 500(1.1)^2
A = 605
CI2 = A - P
CI2 = 605 - 500
CI2 = 105
Similarly, we can calculate the compound interest for each year and the total amount after 12 years.
Year 3: CI3 = 165
Year 4: CI4 = 231.50
Year 5: CI5 = 304.65
Year 6: CI6 = 384.11
Year 7: CI7 = 470.52
Year 8: CI8 = 564.57
Year 9: CI9 = 667.03
Year 10: CI10 = 778.63
Year 11: CI11 = 900.11
Year 12: CI12 = 1032.26
Total Amount after 12 years = (500 + 50) + (500 + 105) + ... + (500 + 1032.26)
Total Amount after 12 years = 500(12) + (50 + 105 + ... + 1032.26)
Total Amount after 12 years = 6000 + (11764.50)
Therefore, the amount standing to his credit one year after he has made his yearly investment for the 12th time is Rs. 11764.50.
- Principal amount (P) = Rs. 500
- Rate of interest (R) = 10% p.a.
- Compound interest is calculated annually
To find:
The amount standing to his credit one year after he has made his yearly investment for the 12th time.
Solution:
1. Calculation of Compound Interest (CI) for each year:
Since the interest is compounded annually, we can use the formula:
Amount (A) = P(1 + R/100)^n
Where,
P = Principal amount
R = Rate of interest
n = Number of years
To find the compound interest for each year, we can subtract the principal amount from the total amount.
Compound Interest (CI) = A - P
2. Calculation of the total amount after 12 years:
Since the person invests Rs. 500 at the end of each year for 12 years, the total amount can be calculated by adding the principal amount and the compound interest for each year.
Total Amount after 12 years = (Principal amount + Compound Interest for Year 1) + (Principal amount + Compound Interest for Year 2) + ... + (Principal amount + Compound Interest for Year 12)
3. Calculation:
Let's calculate the compound interest and the total amount after 12 years.
Year 1:
A = P(1 + R/100)^n
A = 500(1 + 10/100)^1
A = 500(1 + 0.1)^1
A = 500(1.1)
A = 550
CI1 = A - P
CI1 = 550 - 500
CI1 = 50
Year 2:
A = P(1 + R/100)^n
A = 500(1 + 10/100)^2
A = 500(1 + 0.1)^2
A = 500(1.1)^2
A = 605
CI2 = A - P
CI2 = 605 - 500
CI2 = 105
Similarly, we can calculate the compound interest for each year and the total amount after 12 years.
Year 3: CI3 = 165
Year 4: CI4 = 231.50
Year 5: CI5 = 304.65
Year 6: CI6 = 384.11
Year 7: CI7 = 470.52
Year 8: CI8 = 564.57
Year 9: CI9 = 667.03
Year 10: CI10 = 778.63
Year 11: CI11 = 900.11
Year 12: CI12 = 1032.26
Total Amount after 12 years = (500 + 50) + (500 + 105) + ... + (500 + 1032.26)
Total Amount after 12 years = 500(12) + (50 + 105 + ... + 1032.26)
Total Amount after 12 years = 6000 + (11764.50)
Therefore, the amount standing to his credit one year after he has made his yearly investment for the 12th time is Rs. 11764.50.
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A person invests Rs. 500 at the end of each year with a bank which pays interest at 10% p.a. C.I. annually. The amount standing to his credit one year after he has made his yearly investment for the 12thtime is.a)Rs. 11761.20b)Rs. 10000c)Rs. 12000d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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