If I have 10000 dollars and the interest rate is .40% when will my money double if compounded anually?
The formula for compound interest is:
A = P * e^(r*t)
Where A = Amount, P = Principal Amount, r = Interest rate, t = Years to compound
So in your case you want to know when you will have $20,000 so this is what you do:
$20,000 = $10,000 * e^(r*t)
Divide by $10,000 on both sides:
2 = e^(.0040,t)
Take the natural logarithm of each side:
ln(2) = ln(e^(.0040*t))
ln(2) = .0040*t
Divide by .0040
ln(2)/.0040 = t
Solve using calculator:
t = 173 years
It will take approximately 173 years to turn $10,000 to $20,000 with a 0.40% interest rate.