What annual rate of interest is required to double an investment in 3 years?
i tried solving this but got .23 instead of 26%
I know at 7% interest an investment will double in 10 years, but this doesn't help you.
let me see what I can find
is your problem simple interest?
I think so, yes A = Pe^(r)(t)
To find the annual rate of interest required to double an investment in 3 years, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of compounding periods per year
t = the number of years
In this case, we know that the future value A is twice the principal amount P, so A/P = 2. We also know that the investment is made for 3 years, so t = 3.
Substituting these values into the formula, we get:
2 = (1 + r/n)^(n*3)
Now, we can solve for the annual interest rate (r). However, it's important to note that the formula assumes compounding at regular intervals, which is not specified in the question. Therefore, we'll assume it compounds annually (n = 1).
2 = (1 + r/1)^(1*3)
2 = (1 + r)^3
To solve for r, we can take the cube root of both sides:
∛2 = 1 + r
r = ∛2 - 1
Now, we can calculate the value of r:
r = ∛2 - 1
r ≈ 0.2609
Therefore, an annual interest rate of approximately 26.09% is required to double an investment in 3 years.