00:01
This problem says suppose you have the opportunity to invest some money at 15 % compounded continuously.
00:06
If you invest $1 ,000, what would be the value of your investment after five years? round to near cent.
00:12
And then we're also asked how long will it take for our $1 ,000 investment to accumulate $4 ,000? round our answer to two decimal places.
00:20
So first focusing on our first question, what's the value after $1 ,000, of $1 ,000 after five years? we would use the formula y equals p times e raised to the rt since this is compounded continuously.
00:33
And we want to find the final value y.
00:35
So we'll leave y equal to p, which is our principal amount, which is 1 ,000 times e raised to our rate.
00:42
And our rate was given as 15%.
00:43
But in the formula, we need to use the decimal representation, which is 0 .15.
00:48
And that's times t, where t is our time in years, which is five.
00:52
So now we can evaluate this expression in the calculator to get the expectation for how much we would have after five years.
01:00
And that value comes out to 2 ,117 .00001661.
01:09
And we were asked to round to the nearest cent, so zero would not round zero up.
01:14
So we would expect to have $2 ,117 after five years.
01:20
And now to answer our second question, when will $1 ,000 accumulate or get to $4 ,000? and to figure this out, we're going to use the same formula, y equals p times e raised to the rt.
01:31
But this time, we know what we want our final amount to be y, that's $4 ,000.
01:36
And we still have the same principal amount, or p, which is $1 ,000 times e raised to our same rate, the 0 .15, times t, where t is our time in years...