Question 1033122
you deposit 275 paying 4% annual interest compounded continuously.
how many years to have 394.


the continuous compounding formula is f = p * e^(rn)


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.


you are given the annual interest rate.
the time period is therefore in years.


the formula becomes f = p * e^(.04*n)


since f = 394 and p = 275, the formula becomes 394 = 275 * e^(.04*n)


divide both sides of this formula by 275 to get:


394/275 = e^(.04*n)


take the natural log of both sides of this equation to get ln(394/275) = ln(e^(.04*n)).


since ln(e^(.04*n)) is equivalent to .04*n*ln(e), the formula becomes ln(394/275) = .04*n*ln(e).


since ln(e) = 1, the formula becomes ln(394/275) = .04*n


divide both sides of this equation by .04 to get ln(394/275)/.04 = n


solve for n to get n = ln(394/275)/.04 = 8.989495291.


to confirm this is correct, replace n in your original equation to get 294 = 275 * e^(.04*8.989495291).


you will get 394 = 394.


this confirms the solution is correct.