How long will it take for money invested at 3.29% compunded monthly to double?
To find out how long it will take for money invested at a given interest rate to double, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (in this case, double the initial investment)
P = the principal or initial amount invested
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the time in years
In this case, you want to find how long it takes for the investment to double, so A will be equal to 2P. The annual interest rate is 3.29% or 0.0329 as a decimal. The interest is compounded monthly, which means n is equal to 12.
So the equation becomes:
2P = P(1 + 0.0329/12)^(12t)
To solve for t, we can divide both sides by P and then take the natural logarithm of both sides to isolate t.
ln(2) = (0.0329/12) * (12t)
Now, divide both sides of the equation by (0.0329/12):
ln(2) / (0.0329/12) = 12t
Finally, divide both sides by 12 to solve for t:
t = ln(2) / (0.0329/12)
Calculating this expression will give you the number of years it will take for the investment to double at a 3.29% annual interest rate compounded monthly.