Estimating total postsecondary costs
About this video
The video estimates the total cost of a four-year public university degree when tuition, housing and food rise by 2% each year but other costs stay the same. It adds a growing yearly cost of 26,500 x (1 + 1.02 + 1.02^2 + 1.02^3) to a fixed 4,300 x 4 for books and supplies, giving about $126,422.61.
You'll be able to
- model a cost that grows by a fixed percentage each year using powers of a growth factor.
- separate costs that grow from costs that stay the same.
- calculate the total cost of a multi-year degree with a calculator.
Key words
- Growth factor
- The number you multiply by to grow an amount by a percentage; a 2% increase uses 1.02.
- Postsecondary costs
- The money needed for education after high school, such as tuition, housing, food and books.
- Factor out
- Pull a common number out of several terms so you can write them as one product.
Transcript
- [Instructor] The estimated first year costs at a public four-year university are, so they give us all these costs. Assume only tuition, housing and food increase by 2% each year. All other costs stay the same each year. What is the total cost of completing the degree?
Pause the video, have a go at that. And probably it's good idea to use a calculator for this one. All right, now let's do this together. So the stuff that's increasing every year are the tuition fees, housing and food. So this is a total of 26,500. So that's over on the first year.
The second year, it's going to be 26,500. If we're growing by 2%, that would be times 1.02. Our third year, we'd wanna grow by 2% a year, 2% again. So it would be 26,500 times 1.02 times 1.02 again, which we can just write as 1.02 squared. And then for our final year, it's going to be 26,000, not 25,000, it's going to be 26,500 times 1.02.
We're gonna multiply times 1.02 again to the third power. So if you add up all of those, that's going to be your tuition fees, housing and food. And then our books and supplies, which are, let me do that in a different color just for a little bit of variety. These right over here, which sum up to $4,300, these are going to be the same all four years, so we can just multiply that times four.
Now I could just add the stuff in the blue to the stuff in the purple and I would have my answer. But actually I could manipulate the stuff on the top so it'll be a little bit easier to use my calculator. So let me go back to that blue color. So this stuff up there, let me just rewrite it.
So all of this stuff is the same thing. If I were to factor out a 26,500, it's the same thing as 26,500 times 1 plus 1.02 plus 1.02 squared plus 1.02 to the third power. And this is going just gonna be easier to use my calculator. So let's get my calculator out and I am going to get, so I'll first do, what I would say is probably the more complicated part, which is all of this business.
So let's say 1 plus 1.02 plus 1.02 squared plus 1.02 to the third power. So if I get that, and then I multiply that times 26,500, so times 26,500. And then I like this calculator 'cause I can see everything I'm doing. If I add to that 4,300 times 4, so plus 4,300 times 4, an order of operations, it should do this multiplication first and then that multiplication, and then add everything up together, and I am going to get $126,422.612.
And I'm done.
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