Anthony is asking you to invest in a venture that will double your money in 3 years. Compute the annual rate of return they are promising you?
I just answered a very similar question from Kim right below.
The method to solve this is the same, but you can make up your own numbers: say, 10,000 at the start and 20,000 at the end.
i understand the problem below but how is it related to this problem ...would this answer be 41.42%
Start with 10, finish with 20
after 1 year you have 10*x
after 2 years 10*x*x
after 3 years 10*x*x*x
10 x^3 = 20
x^3 = 2
To compute the annual rate of return, we can use the formula for compound interest. The formula is:
A = P(1+r/n)^(nt)
Where:
A is the future value
P is the principal or initial investment amount
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
In this case, we want to determine the interest rate (r) that will double the investment in 3 years. Let's assume you invest P dollars.
So, the future value (A) is 2P, and we need to find the rate (r).
2P = P(1+r/1)^(1*3)
Now, we can simplify the equation and solve for r.
2 = (1+r)^3
Taking the cube root of both sides:
∛2 = 1 + r
Subtracting 1 from both sides:
r = ∛2 - 1
Therefore, the promised annual rate of return is approximately ∛2 - 1. Evaluating it:
r ≈ 0.259921
So, Anthony is promising you an annual rate of return of approximately 25.99%.