How long, to the nearest day, will it take $25,000 to grow to $500000 at 9% annual interest compounded monthly?
(1+.09/12)^(12x) = 500000/25000
x = 33.411 years
I figure you can calculate the required day
150 days
To calculate the time it takes for $25,000 to grow to $500,000 at 9% annual interest compounded monthly, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = the future value of the investment ($500,000 in this case)
P = the initial principal ($25,000)
r = the annual interest rate (9%, or 0.09)
n = the number of times the interest is compounded per year (monthly in this case)
t = the time in years
First, we need to rearrange the formula to solve for t:
t = (log(A/P))/(n * log(1 + r/n))
Now, let's substitute the given values into the formula:
t = (log(500,000/25,000))/(12 * log(1 + 0.09/12))
Using a scientific calculator and evaluating the logarithms, we find that t is approximately 6.405.
Finally, to get the answer to the nearest day, we multiply the time in years by 365 (as there are 365 days in a year):
t (in days) = 6.405 * 365
Therefore, it will take approximately 2341 days (rounded to the nearest day) for $25,000 to grow to $500,000 at 9% annual interest compounded monthly.