Question 1135489
the continuous compounding formula is f = p * e^(r * n)


f is the future value.
p is the present value
r is the interest rate per time period.
n is the number of time periods.


in your problem:


f = 22000
p = 18000
n = 5
r = what you want to find.


the formula becomes 22000 = 18000 * e^(5r)


divide both sides of the equation by 18000 to get 22000 / 18000 = e^(5r)


take the natural log of both sides of this equaiton to get ln(22000 / 18000) = ln(e^(5r)).


since ln(e^(5r) is equal to 5r * ln(e) and since ln(e) is equal  to 1, then ln(e^5r)) becomes 5r.


your equaation becomes ln(22000/18000) = 5r


solve for r to get r = ln(22000/18000) / 5 = .0401341391.


that's your continuous compounding rate per year.


confirm by evaluating the original equation to get 22000 = 18000 * e^(.0401341391 * 5) which results in 22000 = 22000


your solution is that the continuous compounding interest rate per year is equal to 4.01% when expressed as a percent rounded to 2 decimal digits.