Question 1198391
you can use a financial calculator or you can use the following formula.
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.


in your problem:
f = 5000
p = 3000
r = .03/12
n = number of months.


formula becomes:
5000 = 3000 * (1 + .03/12) ^ n
divide both sides of the equation by 3000 to get 5/3 = (1 + .03/12) ^ n
simplify to get 5/3 = 1.0025 ^  n
take the log of both sides of the equation to get:
log(5/3) = log(1.0025^n) which becomes:
log(5/3) = n * log(1.0025)
divide both sides of the equation by log(1.0025) to get:
log(5/3) / log(1.0025) = n
solve for n to get:
n = 204.585556.
confirm by replacing n with that and solving for f in the original equation to get:
f = 3000 * (1 + .03/12) ^ 204.585556 = 5000


the 3000 will grow to 5000 in 204.585556 months = 17.04879634 years.


if you used a calculator such as the one at <a href = "https://arachnoid.com/finance/" target = "_blank">https://arachnoid.com/finance/</a>, you would get n = 204.59.
that's the same answer as from the formula, except rounded to 2 decimal places.


here are the results from using that calculator.


<img src = "http://theo.x10hosting.com/2022/111902.jpg">


since the interest rate is compounded monthly, then you need to get the monthly interest rate and you are solving for the number of months.