FIN 16 Calculating the Rate of Return

Let's have a look at problem three, two, a, this problem has us calculating the rate of return a little harder than problem three, one, but let's jump into it. You lend your friend 400 bucks today. They promised to give you 500 bucks a year from today. Uh, what's the rate of return on this? If you give them $400 today, you get 500 back in a year. What, uh, what's your return? So I think you can intuit the return just with your intuition. You can say, well, I went from 400 to 500. That's a hundred dollars in interest on a $400 investment. That's a hundred over 400, 25% return, but let's kind of math this out. And that's, I think that's the correct answer. Let's math it out with, uh, the formula that we learned from our previous video. So we know if I invest $400 today, I multiply it by one plus the rate of interest. That's what we're solving for to the power of the number of periods. In this case, it's one year. So it's one compounding period. Um, and that's going to equal 500, the future value of my money. Okay. So I divide 500 divided by 400 stuff onto the other side. So 500 divided by 400. So now I have, uh, one plus R to the power of one equals 1.25. I divided 400 off of both sides and any of the power of one is just itself. So it's just one plus R equals 1.25. Subtract R from both sides. I get R equals 0.25. Okay. So I've done it sort of with the math. Now, one year from now, I think you can just do it the quick, easy way I did it, but very likely you'll be given multiple year situations. And if that's the case, you're going to need math. You're going to need the formula on your side. Uh, so it says, assume you lend them $400 today and they pay back the 500 in four years. So it's not one year from now. They hold onto the money for four years and they give you 500. So you earned a hundred dollars of interest over four years, not over one year. What does that look like? Well, same formula. You go 400. That's the value of the money today. Times one plus a rate of interest to the power, not of one now to the power of four equals 500. So, uh, divide both sides by 400. I get one plus R to the power of four equals, um, 1.25. Now here's where you need a bit of algebra skill that I honestly lack. What you end up doing is you say, well, this is to the power of four. And I want to get rid of this exponent. You raise both sides to the power of one fourth. So you end up going one plus R to the power of four. But if I raised this power of one fourth, I get rid of it equals 1.25 to the power of one fourth. Um, okay. So let's do 1.25 to the power of one fourth, 1.25. I hit this Y to the X button to the power of one fourth is 0.25. I have to put it in a decimal here. So 1.25 raised to the power of 0.25 is 1.05737. So I get one plus R equals 1.05737. Subtract one from both sides. I get R equals 0.05737 and we solved it. Um, so R equals 5.737%. Okay. That is the correct answer. And we've done it with formulas. This one might be one I would want to do in a financial calculator. Cause for me, everything's okay. Except for this step where we raise everything by a power of a quarter to get rid of that exponent. You know, if you practice it, certainly you can get it, but it's, I don't know. I'm just not that algebraically talented. And so once I get to something like where it has me calculating rates, I end up leaning on my BA two plus my financial calculator. You may be allowed to do that. If you're not allowed to do that, you know, now's the time to say goodbye. Goodbye. But if you are, uh, using a financial calculator, here's how you would solve with a financial calculator. And I do think this is easy. I do think it is a time-saving step. So the number of periods here, we're just going to do part B. The number of periods is four. The interest rate per period is what we're solving for our present value. We're going to give up $400 now with the expectation of getting $500 in the future. And there are no interim payments, which we will get into. It's a big part of a corporate finance class. But when we're introducing the concept, uh, we don't have any payments. And so payments at the beginning, no, there are no little payments, uh, going back and forth. Okay. So I clear my memory. I go second function, clear TVM. I go second function, clear work. I hit the CEC button a bunch of times. Four and I Y I don't know. PV 400, negative 400, negative PV zero PMT. You don't need to enter that one. If you've cleared your memory properly, 500 FV. And then I say, compute the I Y and I get 5.737. So we solved this one two ways. I think it was a little quicker in the old BA two plus. It's going to depend what your professor allows. If your instructor lets you use a financial calculator, I do recommend using them. I think it's going to save you a lot of time and effort, especially when we get into more complicated annuities and things like that. But that's all for a future video for now on your way out of here. Smash one of those buttons. Is that the verb? I think the verb is smash, smash one of those two buttons for me. Have a great day. I'll talk to you soon. Bye-bye.