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If Rs 1000 is to be invested at interest rate of 5% and after 10 years, total interest is added to the principal, then the total number of years from beginning in which it will amount to Rs 2000 is
- a)50/3year
- b)65/4year
- c)16 year
- d)11 year
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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If Rs 1000 is to be invested at interest rate of 5% and after 10 years...
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If Rs 1000 is to be invested at interest rate of 5% and after 10 years...
Understanding the problem:
To find the total number of years it will take for an investment of Rs 1000 at an interest rate of 5% to amount to Rs 2000, we need to consider the concept of compound interest.
Solution:
- Let's assume the total number of years required for the investment to amount to Rs 2000 is x years.
- Using the compound interest formula: A = P(1 + r/n)^(nt), where:
- A is the amount after t years
- P is the principal amount (Rs 1000)
- r is the interest rate (5% or 0.05)
- n is the number of times interest is compounded per year (considered annually in this case)
- t is the total number of years (x years in this case)
- Given that the total interest is added to the principal after 10 years, the amount after 10 years will be Rs 1000 + (1000 * 0.05 * 10) = Rs 1500.
- Now, we need to find the value of x such that the amount after x years is Rs 2000.
- Plugging in the values, we get: 2000 = 1000(1 + 0.05)^(x)
- Simplifying the equation, we get: 2 = 1.05^x
- Taking the log on both sides, we get: log(2) = x * log(1.05)
- Solving for x, we get: x = log(2) / log(1.05) ≈ 50/3 years
Therefore, the total number of years required for the investment to amount to Rs 2000 is approximately 50/3 years.
To find the total number of years it will take for an investment of Rs 1000 at an interest rate of 5% to amount to Rs 2000, we need to consider the concept of compound interest.
Solution:
- Let's assume the total number of years required for the investment to amount to Rs 2000 is x years.
- Using the compound interest formula: A = P(1 + r/n)^(nt), where:
- A is the amount after t years
- P is the principal amount (Rs 1000)
- r is the interest rate (5% or 0.05)
- n is the number of times interest is compounded per year (considered annually in this case)
- t is the total number of years (x years in this case)
- Given that the total interest is added to the principal after 10 years, the amount after 10 years will be Rs 1000 + (1000 * 0.05 * 10) = Rs 1500.
- Now, we need to find the value of x such that the amount after x years is Rs 2000.
- Plugging in the values, we get: 2000 = 1000(1 + 0.05)^(x)
- Simplifying the equation, we get: 2 = 1.05^x
- Taking the log on both sides, we get: log(2) = x * log(1.05)
- Solving for x, we get: x = log(2) / log(1.05) ≈ 50/3 years
Therefore, the total number of years required for the investment to amount to Rs 2000 is approximately 50/3 years.
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