Question 471981
If the interest is compounded continuously, we use this formula to determine the future value:
{{{FV = Pe^Yr}}} where P = the initial principal, Y = the number of years, r = interest rate
If the investment doubles, FV = 2P, so we can write
{{{2P = Pe^Yr}}}
{{{2 = e^(0.0525Y)}}}
Take the natural log of both sides to get rid of the exponential, and solve for y:
{{{ln 2 = 0.0525Y}}}
{{{Y = ln 2/0.0525}}}
This gives Y = 13.203 years