Answer:
the approximate rate of interest is 0.414, or 41.4%.
Step-by-step explanation:
The rate of interest can be calculated using the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount of money (double the original amount)
- P is the principal amount (the amount Anita borrowed)
- r is the annual interest rate (what we are trying to find)
- n is the number of times the interest is compounded per year (this is not given, so we'll assume it's compounded annually)
- t is the number of years (6 years in this case)
In this problem, Anita borrowed the money from a bank and it will be double within 6 years. This means the final amount, A, will be two times the principal amount, P.
So, we can write the equation as:
2P = P(1 + r/1)^(1*6)
Simplifying further:
2 = (1 + r)^6
To find the value of r, we need to isolate it on one side of the equation. Taking the sixth root of both sides, we have:
√2 = 1 + r
Subtracting 1 from both sides, we get:
r = √2 - 1
Now we can find the approximate value of r using a calculator or by using the value of √2 as 1.414.
r ≈ 1.414 - 1
r ≈ 0.414
Therefore, the approximate rate of interest is 0.414, or 41.4%.
