Question 1178093
the 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.


in your problem:


f = 19450
p = 15000
r = 14% / 100 = .14 / 12 = .01166666667 per month.
n = the number of months you want to find.


the formula becomes 19450 = 15000 * (1 + .01166666667) ^ n


divide both sides of the equation by 15000 to get:
19450/15000 = (1 + .01166666667) ^ n
take the log of both sides of the equation to get:
log(19450/15000) = log((1 + .01166666667) ^ n)
since log(x^n) = n * log(x), this becomes:
log(19450/15000) = n * log(1.01166666667)
divide both sides of the equation by log(1.01166666667) to get:
log(19450/15000) / log(1.01166666667) = n
solve for n to get:
n = 22.39795036 months.


confirm this is correct by replacing n in the original equation with that to get:
f = 15000 * (1 + .01166666667) ^ 22.39795036 = 19450.


this confirms the solution is correct.


the solution is 22.39795036 months for 15000 to grow to 19450 at 14% interest per year compounded monthly.


you could also have used an online financial calculator to get the same results.


here are the inputs to that calculator.


<img src = "http://theo.x10hosting.com/2021/040501.jpg">


here is the output from that calculator.


<img src = "http://theo.x10hosting.com/2021/040502.jpg">


the calculator uses the percent rather than the rate.
the calculator rounds the answer to 2 decimal places.