You invest $4,545 in Clutch Bank today earning a juicy 10% ann...

Question

You invest $4,545 in Clutch Bank today earning a juicy 10% annual interest. What is the value of your investment in one year? What is the value of the investment after two years?

Accepted Answer

Alright. Let's try this. You invest $4,545 in clutch bank today, earning a juicy 10% annual interest. What is the value of your investment in 1 year? What is the value of Alright? So we're gonna deal with these separately, but what I'm gonna do first is I'm gonna draw this on a timeline just because it helps us visualize what's going on. Okay? So this is right now, year 0, 1 year from now, and then 2 years from now. So right now, you're investing $4,545 and it's going to earn 10% and what's it going to be worth in 1 year? And then we also want to know what it's going to be worth in 2 years, right? So that's kinda what's going on here. We're taking this money and we're compounding it into the future, right? So let's go ahead and use our time value of money equation and let's fill in our time line here. So we got the future value which is what we're gonna solve for. Let me first before we get into that, let me say, 1 year. So this is 1 year when we're compounding for 1 year and then we'll do it for 2 years. Okay? So the future value is gonna equal the present value of 4,545 times 1 plus r, right? Present value times 1 plus r and our r, in this case, was 10%, right? This, we invested this is our present value, right? Because we invested it right now. You invested it today, so its present value is 4545 and that is our interest rate is our 10%, which we need to put in as a decimal. 1 plus 0.10 and what's going to be our n in this case? Our exponent of n. Well, since it's 1 year, our exponent is 1, right? So there's not really an exponent in this case because it's just 1 year. So future value it's just gonna be 4545 times 1.10. Okay. Let's see what that gives us. 4545 times 1.1, well, it's approximately $5,000. We're gonna say $5,000 here, we're gonna round it off and that's what it's gonna be worth in 1 year, okay? So that's what we'll put in right here. After 1 year, it's worth $5,000. Let's do the same thing for 2 years. So same equation, future value equals we have the same present value of 4545 times the same interest rate 0.10, but now we're compounding it for 2 years, right? It's not just 1 so our exponent is 2 in this case. So what I would do is I would do the exponent part first, right? We wanna do the parenthesis 1.1 when we do our order of operations. 1.1 times 1.1, right? That's our exponent. So 1.1 squared is 1.1 times 1.1 and then we're gonna multiply that by 4,545 and it comes out to approximately $5,500 here, right? If we were to round it off, okay? So after 2 years it's worth 5,500 and that should make sense. Also, if you think about at 1 year, if we look at our 1 year amount of 5,000, right? We had 5,000 at one point in time and we're gonna earn interest for 1 year, right, from 5,000 in year 1 to year 2, well, it's earning 10% interest. Right? So the 1 plus the 10%. Whoops. 1 plus that 10%, well, 5,000 times the 1.1, guess what? That's also 55100. So that makes sense, right? Because we compounded it for 1 year and then we had 5,000. We compounded for 1 more year and we get to 55100. So we could we have that shortcut where we can just compound for 2 years when we use the exponent. Alright? But that's just how interest works and time passes and we just earn interest on the interest. So that's about it for this one, right? We started with 4545, after 1 year it's worth 5,000 and after 2 years, it's worth 5,500. Cool? So one more, kind of logical approach to this. If you know that this interest rate is 10%, right now I make you the offer. If I were to say to you, based on this information right here. I'm going to offer you $4,545 today, or I'll offer you $5,500 2 years from now. Which one do you want? Do you want $4,545 today? Or $5,502 years from now? Well, the answer here is actually that you should be indifferent. To you, they should pretty much mean the same thing to you. Maybe you'll take the 4,545 today, but the idea here is that they're worth the same amount essentially. Because that 5,502 years from now, if you were to discount it 2 years, well it would be worth 4,545 when you take out the interest. If you take the 4,545 and you invest it for 2 years, guess what? It's worth the same thing as if I paid you 5,500 2 years from now. So the idea is, that these are basically the same amount of money. At this interest rate, me offering you 4 1,545 today or me offering you $55100 2 years from now, they're basically the same thing, alright? That's kind of the tricky concept here that a lot of students struggle with. Is that this is actually the same amount of money when we deal with the interest that's being put into it, alright? So let's go ahead and move on to the next video.

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You invest \$4,545 in Clutch Bank today earning a juicy 10% annual interest. What is the value of your investment in one year? What is the value of the investment after two years?

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