00:01
In this question we ask, in how many months will money double at 8 % compounded monthly? so what we're going to do is use the following formula.
00:09
A is equal to p times the quantity of 1 plus r over n raised to the power of nt.
00:19
Now we're going to be solving for our t.
00:24
Now this formula is given in years, so after i get the number of years, i'm just going to convert into a number of months.
00:31
So if p is my starting amount and i want the money to double, my ending amount is going to be 2p.
00:40
So we're going to have 2p equals p times the quantity of 1 plus r.
00:46
Now my r this time is .08.
00:50
That's 8 % expressed as a decimal.
00:55
This is divided by n.
00:57
Now my n this time is 12 because we're compounding 12 times per year if we compound monthly.
01:03
And then this is to the power of 12 times t.
01:08
So at this point i can divide both sides by p.
01:11
I'm going to be solving for t.
01:14
I'm getting two equals.
01:16
Now inside my parentheses i'm going to have 1 plus .08 over 12, which converts nicely as 151 over 50 as a fraction.
01:29
So this is 151 over 50 raised to the power of 12t...