00:01
So in this problem, we're told that somebody invested $5 ,000 for seven years, and at the end of seven years, they took out $7 ,880.
00:09
So they want us to find the interest rate if it was compounded continuously.
00:14
Well, we have a formula to help us do this.
00:16
It says that a of t is equal to a sub zero times e, the constant, raised to the rt power.
00:24
A of t represents the balance after a certain number of years.
00:27
So in this case, our new balance, a of t, would be 7 ,880 .87.
00:34
A sub -zero is the initial amount invested, which in this case was $5 ,000.
00:39
E is a constant, so we'll bring that down.
00:41
R is what we're looking for, and t is equal to 7.
00:45
So now we just have to solve for r.
00:47
So remember, we're never going to type anything into our calculator until the very end.
00:51
So first, we're going to go ahead and divide both sides by 5 ,000.
00:55
So that leaves us with $7 ,880 .87 divided by 5 ,000.
01:02
And this is equal to e to the 7r power.
01:05
So because our base is e, what i'm going to do is take the natural log of both sides...