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The C.I on Rs. 16000 for 1 ½ years at 10% p.a payable half -yearly is
- a)Rs. 2222
- b)Rs. 2522
- c)Rs. 2500
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The C.I on Rs. 16000 for 1 ½ years at 10% p.a payable half -yearl...
- Principal (P): Rs. 16,000
- Rate of Interest (R): 10% per annum (compounded half-yearly)
- Time Period (t): 1½ years
Formula for Compound Interest:
A = P × (1 + R/100)n
Where:
- A = Amount after n periods
- P = Principal
- R = Rate of interest per period
- n = Number of periods (half-yearly)
Step-by-Step Calculation:
Step 1: Convert the rate to half-yearly
Rate per half-year = 10% / 2 = 5%
Step 2: Apply the Compound Interest formula
A = 16000 × (1 + 5/100)3
A = 16000 × (1 + 0.05)3
A = 16000 × 1.157625
A ≈ 18522
A = 16000 × (1 + 0.05)3
A = 16000 × 1.157625
A ≈ 18522
Step 3: Calculate Compound Interest (C.I.)
C.I. = A - P
C.I. = 18522 - 16000
C.I. ≈ 2522
C.I. = 18522 - 16000
C.I. ≈ 2522
Final Answer:
- Compound Interest (C.I.): Rs. 2522
Most Upvoted Answer
The C.I on Rs. 16000 for 1 ½ years at 10% p.a payable half -yearl...
Given:
Principal amount (P) = Rs. 16000
Time (t) = 1 year
Rate of interest (R) = 10% p.a
Interest is payable half-yearly. Therefore, the rate of interest for each half-year is:
R/2 = 10/2 = 5%
We need to calculate the compound interest for 1 year, which means there will be two half-yearly periods.
Formula for calculating compound interest:
A = P(1 + R/100)^n
Where,
A = Amount
P = Principal
R = Rate of interest
n = Time period
Calculation:
For the first half-year:
Amount after the first half-year = P(1 + R/100)^n
= 16000(1 + 5/100)^1
= 16000(21/20)
= Rs. 16800
Interest for the first half-year = Amount - Principal
= 16800 - 16000
= Rs. 800
For the second half-year:
Principal = Amount from the first half-year = Rs. 16800
Amount after the second half-year = P(1 + R/100)^n
= 16800(1 + 5/100)^1
= 16800(21/20)
= Rs. 17640
Interest for the second half-year = Amount - Principal
= 17640 - 16800
= Rs. 840
Total interest for the year = Interest for first half-year + Interest for second half-year
= 800 + 840
= Rs. 1640
Therefore, the compound interest on Rs. 16000 for 1 year at 10% p.a, payable half-yearly is Rs. 1640.
Option B, Rs. 2522, is not the correct answer.
Principal amount (P) = Rs. 16000
Time (t) = 1 year
Rate of interest (R) = 10% p.a
Interest is payable half-yearly. Therefore, the rate of interest for each half-year is:
R/2 = 10/2 = 5%
We need to calculate the compound interest for 1 year, which means there will be two half-yearly periods.
Formula for calculating compound interest:
A = P(1 + R/100)^n
Where,
A = Amount
P = Principal
R = Rate of interest
n = Time period
Calculation:
For the first half-year:
Amount after the first half-year = P(1 + R/100)^n
= 16000(1 + 5/100)^1
= 16000(21/20)
= Rs. 16800
Interest for the first half-year = Amount - Principal
= 16800 - 16000
= Rs. 800
For the second half-year:
Principal = Amount from the first half-year = Rs. 16800
Amount after the second half-year = P(1 + R/100)^n
= 16800(1 + 5/100)^1
= 16800(21/20)
= Rs. 17640
Interest for the second half-year = Amount - Principal
= 17640 - 16800
= Rs. 840
Total interest for the year = Interest for first half-year + Interest for second half-year
= 800 + 840
= Rs. 1640
Therefore, the compound interest on Rs. 16000 for 1 year at 10% p.a, payable half-yearly is Rs. 1640.
Option B, Rs. 2522, is not the correct answer.
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