What nominal annual rate of interest compounded yearly is required to double an investment in 13 years?
2 = (1+r)^13
2^(1/13) = 1+r
r = 2^(1/13)-1 = 5.48%
To find the nominal annual rate of interest compounded yearly required to double an investment in 13 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the future value of the investment
P = the principal (initial investment)
r = nominal annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, we want to double the investment, so A = 2P. And since the interest is compounded yearly, n = 1.
Now we can substitute the values into the formula:
2P = P(1 + r/1)^(1*13)
Simplifying:
2 = (1 + r)^13
To solve for r, we need to isolate it. Taking the 13th root on both sides:
(1 + r) = cuberoot(2)
Subtracting 1 from both sides:
r = cuberoot(2) - 1
To find the nominal annual rate of interest, we can convert the value to a percentage:
r = (cuberoot(2) - 1) * 100
Using a calculator, we can calculate the approximate value for r:
r ≈ 7.18%
Therefore, a nominal annual rate of interest of approximately 7.18% compounded yearly is required to double an investment in 13 years.