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 see how you guys did here. 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 the investment after 2 years? So let's go ahead and check this out. 1st, let's draw a timeline. So we kind of see what's going on here. This is a pretty simple problem. So the timeline is not totally necessary, but let's get that practice in. 012, right? We're talking about 2 total years and we've got $4,545 today. So what's it gonna be worth after 1 year and what's it gonna be worth after 2 years? That's the questions here. Right? That's what it's asking us and we've got a 10% interest rate, 10% interest rate at the Clutch Bank. So let's go ahead and compound it for 1 year, right? It's asking us what is the value in 1 year? So it's asking us for a future value, right? So we can use our equation, future value equals present value times 1 plus R to the end, right? That is our equation and let's plug in what we know. So let's put the future value 1. I'm going to put future value 1 because we're talking about 1 year here. So future value 1 is gonna equal the present value of 400,545, right? That's what it's worth today. Well, what's it gonna be worth in the future? 1 plus our interest rate of 10% which is going to be 0.10 to the first power, right? Our exponent is just going to be 1 in this case because it's just 1 year into the future. So, if we finish this up, we've got 4,545 times 1.10, right? So notice what's happened here. We've got the 1 which is the original value. That's the principal value. 4,545 times 1 is the original value and then 4,545 times 0.10, that's the interest that you earn. So that's why we can just take the 1 plus whatever the decimal is, right? Whatever that interest rate is. So 4545 times 1.10. Well, we're gonna round this off and it's gonna come out to approximately $5,000 So after 1 year, your $4,545 is now worth $5,000 Right? So now, let's go ahead and do after 2 years. Future value after 2 years, well, we do the same thing. $4,545 times 1.10, right? 1 plus 10%, 1.10, but now it's to the second power, right? We're going to square it here. So that's 4545 times 1.1 times 1.1 again, right? Because we're earning interest twice. We're going to get the 10% twice. So what do we get here? If we do that math, 1.1 times 1.1 is 1 point 2 one times 4,545. It's going to come out to approximately 5,500 in that case, right, 5,500. Cool? And notice what we could do. We could have taken if we took the value after 1 year, 5,000 and multiplied it by 1.1, give it 1 more year's of interest, right? We had already added 10% after 1 year. If we add another 10%, well, that's still going to get us to 5,500, right? So it the math makes sense, right? We're just adding the interest, 10% interest each year to find out what it's worth in the future. Cool? So after 1 year, it's worth $5,000 after 2 years, it's worth $5,500 One more thing before we move on. If we knew that the interest rate was 10% in this market and I told you right now, hey, I'll give you $4,545 today or I'll give you $5,500 2 years from now, which one would you pick? 4,545 today or 5,500 2 years from now? Well, the idea here is that you should technically be indifferent because you could take that 4,005 today, invest it and it would be worth 5,500 2 years from now, right? So they have the same technical, the same value here. If we took that 5,500 and found out what it was worth today by discounting it, well guess what? It would be worth 4,545 because we're taking out the interest. So the idea with time value of money is you would be indifferent about these because of the current interest rate, and what they're worth at those different point in time. Cool? Let's pause here, and let's 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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