Calculating and graphing exponential functions for investing (part 2)
About this video
The video reads a graph showing the value of Avery's and Blake's retirement accounts over time. Blake starts 10 years after Avery and his curve rises faster, but Avery reaches $50,000 first (around year 22) and $100,000 slightly first, while Blake reaches $150,000 first. The narrator infers that Avery probably contributes less each month but benefits from a longer time compounding.
You'll be able to
- read when an account starts growing from a graph of value over time.
- use a graph to compare when two accounts reach a target value.
- explain what a steeper curve suggests about contributions or returns.
Key words
- Exponential growth
- Growth that speeds up over time because earnings are added to the amount that keeps growing.
- Compounding
- Earning returns on both your deposits and the returns you've already earned.
- Rate of return
- How fast an investment grows, usually as a percent per year.
- Retirement account
- An account people pay into over their working life to save for retirement.
Transcript
- [Instructor] The graph shows the value of two retirement accounts over time. How many years after Avery started did Blake start contributing to his retirement account? Who reaches $50,000 first? How about 100,000? Pause the video, have a go at that before we do it together.
Okay, so for the first question, how many years after Avery started did Blake start contributing? Well, we can see the curve for Avery. His retirement account starts building up from time zero, at zero years. I'm assuming this isn't how old Avery is, we're just defining zero to be whenever Avery started.
Maybe he was 25 years old or 35 years old, who knows? But we can see that's when his account starts accumulating money. Now, Blake's is at 10 years, or 10 years after that, we see Blake's account starting to accumulate money. It seems like at a faster rate, so we can talk about that in a second.
Maybe he's either getting a better rate of return or he's putting more money per month into the account. But either way, to the first part, how many years after Avery started did Blake start contributing to his retirement account? 10 years. We see that right over here.
This is a 10-year difference. Who reaches $50,000 first? Well, let's look up here at $50,000, and let's think about which curve gets there first. Well, Avery gets there after, let's call it, or not after it, at year, looks like year maybe 22, while Blake gets there at year, this looks like maybe year 24 or 23.
So Avery definitely gets to $50,000 first. Now, what about $100,000? Well, let's look over here. This is really close. They're almost, it looks like it'd be a matter of months different, but it looks like Avery gets there still a little bit, a little bit earlier.
You can zoom in on this video and see that. If you said who gets to $150,000 first, which they're not asking us, but that's an example where we see that we can see that Blake does get there a little bit earlier because maybe Blake is contributing more every month or maybe getting a better return.
But either way, that's what's happening over there. But we answered their question. For these two, it's Avery in both of these situations. So it's interesting. Well, we don't know exactly how much Avery's putting in. If we assume that they're getting the same rate of return and it's compounding the same way, just looking at the initial curves, it's probably safe to assume that Avery is contributing less each month, but it's compounding in a way that it takes a long time for Blake to catch up, even though he might be putting more every month.
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