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A sum of money doubles itself in 4 years of compound interest. In what time will it amount to 8 times itself at the same rate of interest?
- a)8 years
- b)12 years
- c)16 years
- d)20 years
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A sum of money doubles itself in 4 years of compound interest. In what...
Given Data:
- Money doubles itself in 4 years of compound interest
- We need to find the time at which the money will amount to 8 times itself at the same rate of interest
Calculation:
- Let's assume the initial amount of money is 'P'
- After 4 years, the money doubles itself, so the amount becomes 2P
- Now, we need to find the time at which the amount will become 8P
Using the formula for compound interest:
- For the money to double in 4 years, the compound interest rate per year would be 100% / 4 = 25%
- Let 'n' be the number of years for the amount to become 8 times itself
- Using the formula A = P(1 + r/100)^n, we have:
8P = P(1 + 25/100)^n
8 = (1.25)^n
2^3 = (1.25)^n
(2^3) / (2^3) = (1.25)^n / 8
1 = 1.25^n / 8
8 = 1.25^n
2^3 = 1.25^n
(2^3) / (5^3) = 1.25^n / 5^3
2/5 = 1.25^n / 5^3
2/5 = (5/4)^n / 5^3
2/5 = 5^(n-3) / 4^n
2 * 4^n = 5 * 5^(n-3)
8 * 4^(n-3) = 5^(n-2)
- By observation, we can see that n = 12 satisfies the equation
- Therefore, the money will amount to 8 times itself in 12 years at the same rate of interest
Final Answer:
- The time at which the money will amount to 8 times itself at the same rate of interest is 12 years
- Money doubles itself in 4 years of compound interest
- We need to find the time at which the money will amount to 8 times itself at the same rate of interest
Calculation:
- Let's assume the initial amount of money is 'P'
- After 4 years, the money doubles itself, so the amount becomes 2P
- Now, we need to find the time at which the amount will become 8P
Using the formula for compound interest:
- For the money to double in 4 years, the compound interest rate per year would be 100% / 4 = 25%
- Let 'n' be the number of years for the amount to become 8 times itself
- Using the formula A = P(1 + r/100)^n, we have:
8P = P(1 + 25/100)^n
8 = (1.25)^n
2^3 = (1.25)^n
(2^3) / (2^3) = (1.25)^n / 8
1 = 1.25^n / 8
8 = 1.25^n
2^3 = 1.25^n
(2^3) / (5^3) = 1.25^n / 5^3
2/5 = 1.25^n / 5^3
2/5 = (5/4)^n / 5^3
2/5 = 5^(n-3) / 4^n
2 * 4^n = 5 * 5^(n-3)
8 * 4^(n-3) = 5^(n-2)
- By observation, we can see that n = 12 satisfies the equation
- Therefore, the money will amount to 8 times itself in 12 years at the same rate of interest
Final Answer:
- The time at which the money will amount to 8 times itself at the same rate of interest is 12 years
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Community Answer
A sum of money doubles itself in 4 years of compound interest. In what...
Let the sum = X
After 4 years = 2X
After 4 more years = 2X × 2 = 4X
After 4 more years = 4X × 2 = 8X
So the answer = 4 + 4 + 4 = 12 years
Hence, Option B is correct.
After 4 years = 2X
After 4 more years = 2X × 2 = 4X
After 4 more years = 4X × 2 = 8X
So the answer = 4 + 4 + 4 = 12 years
Hence, Option B is correct.
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A sum of money doubles itself in 4 years of compound interest. In what time will it amount to 8 times itself at the same rate of interest?a)8 yearsb)12 yearsc)16 yearsd)20 yearsCorrect answer is option 'B'. Can you explain this answer?
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