Question 1136388
the continuous compounding formula is f = p * e ^ (r * n)


f if the future value
p is the present value
e is the scientific constant of 2.718281828.....
r is the rate per time period.
n is the number of time periods.


in your problem:


p = 2900
f = 2 * 2900
r = 3.5% / 100 = .035 per year.
n = the number of years you want to find.


the formula becomes:


2 * 2900 = 2900 * e ^ (.035 * n)


simplify this to get:


5800 = 2900 * e ^ (.035 * n)


divide both sides of this equation by 2900 to get:


2 = e ^ (.035 * n)


take the natural log of both sides of this equation to get:


ln(2) = ln(e ^ (.035 * n)


since ln(a^b) = b*ln(a), this equation becomes:


ln(2) = .035 * n * ln(e).


since ln(e) = 1, this equation becomes:


ln(2) = .035 * n


divide both sides of this equation by .035 to get:


ln(2) / .035 = n


solve for n to get:


n = ln(2) / .035 = 19.80420516.


confirm by replacing n in the original equation of 5800 = 2900 * e ^ (.035 * n) to get:


5800 = 2900 * e ^ (.035 * 19.80420516) which becomes:


5800 = 5800


this confirms the solution is correct.


the solution is that investment will double in 19.8 years rounded to the nearest tenth of a year.