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Ramesh borrowed Rs. 11000 from a private lender who charge compound interest rate 20% per annum but he calculates the interest half-yearly. Find out amount paid by Ramesh in one and half year?
- a)14000
- b)14300
- c)13310
- d)14641
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Ramesh borrowed Rs. 11000 from a private lender who charge compound in...
GIVEN:
Principal = Rs. 11000
Rate = 20% yearly
Time = One and half year
Principal = Rs. 11000
Rate = 20% yearly
Time = One and half year
FORMULA USED:
Amount = P(1 + R/100)n
Amount = P(1 + R/100)n
CONCEPT:
As interest compounded half-yearly, number of times principle will compound 3 times in one and half year.
As interest compounded half-yearly, number of times principle will compound 3 times in one and half year.
CALCULATION:
R = 20% yearly
∴ R = 10% half-yearly
A = 11000(1 + 10/100)3
⇒ 11000 × (1331/1000)
⇒ Rs. 14641
R = 20% yearly
∴ R = 10% half-yearly
A = 11000(1 + 10/100)3
⇒ 11000 × (1331/1000)
⇒ Rs. 14641
Most Upvoted Answer
Ramesh borrowed Rs. 11000 from a private lender who charge compound in...
Given:
Ramesh borrowed Rs. 11000 from a private lender.
Interest rate: 20% per annum (compounded half-yearly)
To find:
Amount paid by Ramesh in one and a half years.
Solution:
To find the amount paid by Ramesh in one and a half years, we need to calculate the compound interest and add it to the principal amount.
Step 1: Calculate the interest for the first half-year:
Principal amount (P) = Rs. 11000
Rate of interest (R) = 20% per annum
Time (T) = 1/2 year
Compound Interest (CI) = P * (1 + R/100)^T - P
CI = 11000 * (1 + 20/100)^1/2 - 11000
CI = 11000 * (1.1)^1/2 - 11000
CI = 11000 * (1.0488) - 11000
CI = 11436.8 - 11000
CI = Rs. 436.8
Step 2: Calculate the interest for the second half-year:
Principal amount (P) = Rs. 11000 + Rs. 436.8 (previous CI)
Rate of interest (R) = 20% per annum
Time (T) = 1/2 year
Compound Interest (CI) = P * (1 + R/100)^T - P
CI = (11000 + 436.8) * (1 + 20/100)^1/2 - (11000 + 436.8)
CI = 11436.8 * (1.1)^1/2 - 11436.8
CI = 11436.8 * (1.0488) - 11436.8
CI = Rs. 441.6
Step 3: Calculate the interest for the third half-year:
Principal amount (P) = Rs. 11000 + Rs. 436.8 + Rs. 441.6 (previous CI)
Rate of interest (R) = 20% per annum
Time (T) = 1/2 year
Compound Interest (CI) = P * (1 + R/100)^T - P
CI = (11000 + 436.8 + 441.6) * (1 + 20/100)^1/2 - (11000 + 436.8 + 441.6)
CI = 11436.8 * (1.1)^1/2 - 11436.8
CI = 11436.8 * (1.0488) - 11436.8
CI = Rs. 447.36
Total amount paid by Ramesh:
Total amount = Principal amount + Compound Interest
Total amount = Rs. 11000 + Rs. 436.8 + Rs. 441.6 + Rs. 447.36
Total amount = Rs. 12325.76
Therefore, the amount paid by Ramesh in one and a half years is Rs. 12325.76, which is closest to option (D) 14641.
Ramesh borrowed Rs. 11000 from a private lender.
Interest rate: 20% per annum (compounded half-yearly)
To find:
Amount paid by Ramesh in one and a half years.
Solution:
To find the amount paid by Ramesh in one and a half years, we need to calculate the compound interest and add it to the principal amount.
Step 1: Calculate the interest for the first half-year:
Principal amount (P) = Rs. 11000
Rate of interest (R) = 20% per annum
Time (T) = 1/2 year
Compound Interest (CI) = P * (1 + R/100)^T - P
CI = 11000 * (1 + 20/100)^1/2 - 11000
CI = 11000 * (1.1)^1/2 - 11000
CI = 11000 * (1.0488) - 11000
CI = 11436.8 - 11000
CI = Rs. 436.8
Step 2: Calculate the interest for the second half-year:
Principal amount (P) = Rs. 11000 + Rs. 436.8 (previous CI)
Rate of interest (R) = 20% per annum
Time (T) = 1/2 year
Compound Interest (CI) = P * (1 + R/100)^T - P
CI = (11000 + 436.8) * (1 + 20/100)^1/2 - (11000 + 436.8)
CI = 11436.8 * (1.1)^1/2 - 11436.8
CI = 11436.8 * (1.0488) - 11436.8
CI = Rs. 441.6
Step 3: Calculate the interest for the third half-year:
Principal amount (P) = Rs. 11000 + Rs. 436.8 + Rs. 441.6 (previous CI)
Rate of interest (R) = 20% per annum
Time (T) = 1/2 year
Compound Interest (CI) = P * (1 + R/100)^T - P
CI = (11000 + 436.8 + 441.6) * (1 + 20/100)^1/2 - (11000 + 436.8 + 441.6)
CI = 11436.8 * (1.1)^1/2 - 11436.8
CI = 11436.8 * (1.0488) - 11436.8
CI = Rs. 447.36
Total amount paid by Ramesh:
Total amount = Principal amount + Compound Interest
Total amount = Rs. 11000 + Rs. 436.8 + Rs. 441.6 + Rs. 447.36
Total amount = Rs. 12325.76
Therefore, the amount paid by Ramesh in one and a half years is Rs. 12325.76, which is closest to option (D) 14641.
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Ramesh borrowed Rs. 11000 from a private lender who charge compound interest rate 20% per annum but he calculates the interest half-yearly. Find out amount paid by Ramesh in one and half year?a)14000b)14300c)13310d)14641Correct answer is option 'D'. Can you explain this answer?
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