Question 1179805
formula to use is:


f = p * (1 + 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..


the interest rate per year = 4.18%
divide that by 100 to get an interest rate of .0418 per year.
divide that by 12 to get an interect rate of .0418/12 per month.


f = 36
p = 25


formula becomes:


36 = 25 * (1 + .0418/12) ^ n


divide both sides by 36 to get:


36/25 = (1 + .0418/12) ^ n


take the log of both sides to get:


log(36/25) = log((1 + .0418/12) ^ n)


since log(x^n) = n * log(x), this becomes:


log(36/25) = n * log(1 + .0418/12)


solve for n to get:


n = log(36/25) / log(1 + .0418/12) = 104.8644495.


that's the number of months for 25000 to grow to 36000 at 4.18% per year compounded monthly.


confirm by solving for f with that value of n to get:


f = 25000 * (1 + .0418/12) ^ 104.8644495 = 36000.


answer is confirmed to be correct.


number of months required is 104.8644495.


number of years required is that divided by 12 = 8.730704122.


in order to confrim that to be correct, you need the effective interest rate per year.


that would be equal to (1 + .0418/12) ^ 12 = 1.04261019 minus 1 = .04261019.


confirm by replacing n with the number of years and r with the effective interest rate per year to get:


f = 25000 * (1 + .04261019) ^ 8.738704122 = 36000.