Err will continue where everyone else has left off to show you the solution when working with logarithms just in case you didn’t know. As mentioned, the formula which you will be using is:
5000*(1.08)^n = 7500
(5000 is the original deposit, multiplied by 1.08^n where n represents the number of years passed. 7500 is the target amount you want).
so you take the log of both sides:
log 5000(1.08)^n = log 7500.
then we can rearrange this using the rules that log x^y = y log x and log xy = log x + log y to get:
log 5000 + n log 1.08 = log 7500
we subtract log 5000 from both sides to get:
n log 1.08 = log 7500 – log 5000
this second half of the equation can be rewritten again (using the same idea as the log xy = log x + log y rule mentioned earlier, but swapping the multiplication for division and the addition for subtraction) to get:
n log 1.08 = log 1.5
we then finish by dividing by log 1.08 to get:
n = log 1.5 / log 1.08
then we can solve using a calculator to find the solution of 5.27.
Finally, don’t forget to round up to find your answer :D.