00:03
We are going to find the final amount if $1 ,500 is invested at 7 % interest for 12 years, compounded continuously.
00:13
And to do so, we're going to use the formula a equals p times e to the r times t, where p is your principal or initial amount, r is your annual interest rate as a decimal, and a is that final amount after t years.
00:36
We're using this formula because we are told that the interest was compounded continuously.
00:42
So i've replaced our principal with that $1 ,500.
00:45
E is just a constant.
00:47
R, our rate was 7 % expressed as a decimal that is 0 .07, and t in time was 12 years.
00:55
Our only remaining variable here is a, which is that final amount that we are trying to find, which means that we can throw this entire right -hand side of the equation in terms.
01:05
To a calculator.
01:09
We get out $3 ,474 .55.
01:13
That should make sense.
01:14
This is gaining interest, so this final amount should be more than the initial amount.
01:21
Now we want to find the final amount if $19 ,000 is invested at 2 .5 % interest for 60 years, again, compounded continuously.
01:33
Here we'll use that same formula.
01:35
A equals p times e to the r times t.
01:38
Where a is what we are looking for.
01:41
Our initial amount, p, was $19 ,000 times e to the, we change our rate of 2 .5 to a decimal, 0 .25.
01:52
And our years, our time, this interest is accumulating, is 60.
01:58
Again, we can just throw this entire right -hand side into a calculator.
02:01
Make sure when you're doing this that the entire exponent shows that that is multiplication in the, power...