Question 1189632
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.


when the time periods are in years and the interest rate is 6% per year and the present value is 50,000 and the future value is 89,542, the formula becomes:


89,542 = 50,000 * (1 + .06) ^ n
divide both sides of the equation by 50,000 and simplify the right side of the equation to get:
89,542/50,000 = 1.06 ^ n
take the log of both sides of the equation to get:
log(89,542/50,000) = log(1.06^n) which becomes:
log(89,542/50,000) = n*log(1.06)
divide both sides of the equation by log(1.06) to get
log(89,542/50,000)/log(1.06) = n
solve for n to get:
n = 9.999926243.
replace n in the original equation with that and solve for f to get:
f = 50,000 * 1.06^9.999926243 = 89,542.
this confirms the value of n is good.
your solution is that it will take 9.999926243 years for her money to grow to 89,542.