00:01
An individual has $25 ,000 to invest.
00:03
We're going to put $16 ,000 into a low -risk mutual fund that earns 5 % interest compounded monthly.
00:13
The remainder, which will be $9 ,000, it's going to be in a high yield, which gets 9 .7 % interest compounded continuously.
00:24
So we want to write an equation for the total amount in the two investments after two years.
00:30
So we have two different formulas to look at.
00:33
Here we're going to have a equals p 1 plus r over n to the n t so we're going to have 16 ,000 1 plus 0 .05 over 12 to the 12 t.
00:46
Here we're doing continuous we're going to have this formula.
00:50
So we're looking at 9 ,000 e to the 0 .097 t so our total amount in terms of t is going to be when we add those together.
01:06
Plus the 9 ,000 e to the 097t.
01:10
So there we have our equation.
01:12
Now we want to know a rate of change equation for this amount, which means we need to find the derivative.
01:18
So we're simply going to find the derivative of both pieces.
01:21
So a prime of t, we're going to have 16 ,000.
01:26
We're going to have the same amount...