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In how many minimum number of years will a sum of money be more than double at 15% compound interest rate?
- a)5 years
- b)3 years
- c)2 years
- d)1 year
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In how many minimum number of years will a sum of money be more than ...
Rate = 15%
Let the principal money be P and time be T years.
According to the question,
(1.15)T > 2
Now, substituting values of T
T = 2,
(1.15)2 = 1.3225
T = 3,
(1.15)3 = 1.5208
T = 5,
(1.15)5 = 2.011
For T = 5,
(1.15)T > 2
So, time = 5 years
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In how many minimum number of years will a sum of money be more than ...
Question Analysis:
We are given a compound interest rate of 15% and we need to find the minimum number of years it will take for a sum of money to be more than double. We can solve this problem using the compound interest formula.
Formula:
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
Solution:
We need to find the minimum number of years it will take for a sum of money to be more than double. This means we need to find the value of t when the future value A is greater than 2P.
Let's assume the principal amount P is 1. This means we need to find the value of t when A is greater than 2.
Using the compound interest formula, we have:
A = 1(1 + 0.15/n)^(nt)
To find the minimum number of years, we can start by testing different values of n.
Testing n = 1:
A = 1(1 + 0.15/1)^(1t)
A = 1(1 + 0.15)^t
A = (1.15)^t
For A to be more than 2, we need to find the minimum value of t.
Testing t = 1:
A = (1.15)^1
A = 1.15
Since A = 1.15 is less than 2, we can conclude that it will take more than 1 year for the sum of money to be more than double. Therefore, option D is incorrect.
Testing t = 2:
A = (1.15)^2
A = 1.3225
Since A = 1.3225 is less than 2, we can conclude that it will take more than 2 years for the sum of money to be more than double. Therefore, option C is incorrect.
Testing t = 3:
A = (1.15)^3
A = 1.520875
Since A = 1.520875 is less than 2, we can conclude that it will take more than 3 years for the sum of money to be more than double. Therefore, option B is incorrect.
Testing t = 4:
A = (1.15)^4
A = 1.74900625
Since A = 1.74900625 is less than 2, we can conclude that it will take more than 4 years for the sum of money to be more than double.
Testing t = 5:
A = (1.15)^5
A = 2.0113571875
Since A = 2.0113571875 is greater than 2, we can conclude that it will take at least 5 years for the sum of money to be more than double. Therefore, option A is correct.
Therefore, the minimum number of years
We are given a compound interest rate of 15% and we need to find the minimum number of years it will take for a sum of money to be more than double. We can solve this problem using the compound interest formula.
Formula:
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
Solution:
We need to find the minimum number of years it will take for a sum of money to be more than double. This means we need to find the value of t when the future value A is greater than 2P.
Let's assume the principal amount P is 1. This means we need to find the value of t when A is greater than 2.
Using the compound interest formula, we have:
A = 1(1 + 0.15/n)^(nt)
To find the minimum number of years, we can start by testing different values of n.
Testing n = 1:
A = 1(1 + 0.15/1)^(1t)
A = 1(1 + 0.15)^t
A = (1.15)^t
For A to be more than 2, we need to find the minimum value of t.
Testing t = 1:
A = (1.15)^1
A = 1.15
Since A = 1.15 is less than 2, we can conclude that it will take more than 1 year for the sum of money to be more than double. Therefore, option D is incorrect.
Testing t = 2:
A = (1.15)^2
A = 1.3225
Since A = 1.3225 is less than 2, we can conclude that it will take more than 2 years for the sum of money to be more than double. Therefore, option C is incorrect.
Testing t = 3:
A = (1.15)^3
A = 1.520875
Since A = 1.520875 is less than 2, we can conclude that it will take more than 3 years for the sum of money to be more than double. Therefore, option B is incorrect.
Testing t = 4:
A = (1.15)^4
A = 1.74900625
Since A = 1.74900625 is less than 2, we can conclude that it will take more than 4 years for the sum of money to be more than double.
Testing t = 5:
A = (1.15)^5
A = 2.0113571875
Since A = 2.0113571875 is greater than 2, we can conclude that it will take at least 5 years for the sum of money to be more than double. Therefore, option A is correct.
Therefore, the minimum number of years
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