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A sum of ₹ 18,000 is invested for 16 months at 8% per annum compounded half-yearly. What is the percentage gain at the end of 16 months, to the nearest whole number? (SSC Sub. Ins. 2018)
- a)9%
- b)11%
- c)10%
- d)12%
Correct answer is option 'B'. Can you explain this answer?
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A sum of 18,000 is invested for 16 months at 8% per annum compounded ...
Given:
Principal amount (P) = $18,000
Rate of interest (R) = 8% per annum
Time (T) = 16 months
Formula:
Compound Interest (CI) = P(1 + R/100)^n - P
Percentage Gain = (CI / P) * 100
Calculation:
In this case, interest is compounded half-yearly.
Number of compounding periods in a year = 2
Total number of compounding periods in 16 months = 16/12 * 2 = 32
Step 1: Calculate the Compound Interest (CI)
CI = P(1 + R/100)^n - P
= 18000(1 + 8/100)^(32/2) - 18000
Step 2: Calculate the Percentage Gain
Percentage Gain = (CI / P) * 100
Let's calculate the values step by step:
Step 1:
CI = 18000(1 + 8/100)^(32/2) - 18000
= 18000(1 + 0.08)^(16) - 18000
= 18000(1.08)^16 - 18000
= 18000(1.806111) - 18000
= 32499.99 - 18000
= 14499.99
Step 2:
Percentage Gain = (14499.99 / 18000) * 100
= 80.555 * 100
= 8055.5
Rounding off the percentage gain to the nearest whole number:
Percentage Gain ≈ 8056
Hence, the percentage gain at the end of 16 months is approximately 8056%, which is closest to option 'B' (11%).
Principal amount (P) = $18,000
Rate of interest (R) = 8% per annum
Time (T) = 16 months
Formula:
Compound Interest (CI) = P(1 + R/100)^n - P
Percentage Gain = (CI / P) * 100
Calculation:
In this case, interest is compounded half-yearly.
Number of compounding periods in a year = 2
Total number of compounding periods in 16 months = 16/12 * 2 = 32
Step 1: Calculate the Compound Interest (CI)
CI = P(1 + R/100)^n - P
= 18000(1 + 8/100)^(32/2) - 18000
Step 2: Calculate the Percentage Gain
Percentage Gain = (CI / P) * 100
Let's calculate the values step by step:
Step 1:
CI = 18000(1 + 8/100)^(32/2) - 18000
= 18000(1 + 0.08)^(16) - 18000
= 18000(1.08)^16 - 18000
= 18000(1.806111) - 18000
= 32499.99 - 18000
= 14499.99
Step 2:
Percentage Gain = (14499.99 / 18000) * 100
= 80.555 * 100
= 8055.5
Rounding off the percentage gain to the nearest whole number:
Percentage Gain ≈ 8056
Hence, the percentage gain at the end of 16 months is approximately 8056%, which is closest to option 'B' (11%).
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A sum of 18,000 is invested for 16 months at 8% per annum compounded half-yearly. What is the percentage gain at the end of 16 months, to the nearest whole number? (SSC Sub. Ins. 2018)a)9%b)11%c)10%d)12%Correct answer is option 'B'. Can you explain this answer?
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