you are very close!
When dealing with appreciating value, you have to first convert the percentage to a decimal (divide by 100), then add 1. Without adding 1, you'd simply be calculating what 6.5% of $88,500 is. Adding the 1 is basically "6.5% of $85000 plus $85,000", which gives you a bigger number instead of a smaller one.
So our formula is:
You do not have to use the log function here. We are given that we are looking for the value of the condo after 15 years, so x=15
y = 88500(1.065)15
1.06515 = 2.572
y = 88500*2.572 = $227,607.93
If you'd like to go over how all of this works in more detail, I'd be happy to help out, just let me know!
log is the opposite of an exponential. For example, let's say instead of "what is the value in 2015?", the question instead asked "when will the value of the condo reach $227,607.93?"
We start out with the same formula as before, but instead we plug in $227,607.93 for y.
227607.93 = 88500(1.065)x
2.572 = 1.065x This basically says: 1.065 to the power of what equals 2.572
We would solve for x by writing it like this: Log1.065(2.572) = x
saying this out loud sounds like "log base 1.065 of 2.572 equals x."
in my calculator (ti-84+), there is a "logBASE" function under "MATH". You then type in the numbers just like the formula, and it gives us x = 15.
ln (called natural log) is the same thing, but the base is always e. e is kind of like pi, it's special number that comes up a lot in math to describe exponential growth. e ≈ 2.71828. If you have a graphing calculator, you should have an ex button and an LN button.