FIN 18 Calculating the Number of Periods

Let's have a look at problem three for a thus far, we've been asked to calculate the present value, the future value, the rate of return, or the interest rate. And now we're being asked to do the hardest one, mathematically anyway, the hardest one, the number of periods. So we're given present value number. You invest $50,000 today at an interest rate of 8%. So we're given the rate and it says, how long will it take for this investment to grow to 75,000? So that's the future value. So we've been given everything, but how long, right? The number of periods, this is the hardest one to do. So here's the formula we've been using quite often. This module, the present value, you take the dollar value today times by one plus the rate raised to the power of the number of periods equals our future value. So plugging things in here, it's $50,000 times one plus the rate of interest, 1.08. Our rate is 8% raised to the power of T. That's what we're solving for. We don't know the number of periods equals our future value, 75,000. So we got to solve for T and the fact that we're solving for an exponent brings the math far beyond my puny brain, but I, my understanding reading the textbooks is it's just not an easy solve. The textbooks all say just trial and error to get your answer. So I'll show you what trial and erroring to get our answer looks like here. So I'm going to divide both sides by 50,000 to get the 50,000 off this side. So I have 1.08 to the power of T equals 75 divided by 50, it equals 1.5. Okay. So I need to know, I need to make 1.08 to the power of something equal 1.5. And good news is most calculators will have this Y to the X or some X to the Y button, right? That I'm hovering over right now. Uh, and so I just trial and error. I go, okay, well, 1.08 to the power of three. Is it three years? 1.25. I'm not even close. Okay. 1.08 to the power of six years. Is it six years? Okay. 1.58. I'm too high, right? Cause I want it to be 1.5. I'm shooting for 1.5. So 1.2 is too low. 1.62. I let's go a year less. 1.08 to the power of five. Oh, I'm closer now. 1.47. I want to be at 1.5, but I'm at 1.47. So it's a little bit higher than five years. Uh, 1.08 to the power of 5.2 years. It's a 5.2 years. Well, I'm 1.49. I'm still out there. It's higher than 5.2. 1.08 to the power of 5.3. Now I'm just a little too high. It's somewhere between 5.2 and 5.3 years. 1.08 to the power of 5.25, 1.497. Okay. I'm going to stop there. I'm going to say 1.08. I'm going to say T here just by trial and error. Equals. I'll make it this way because we're not quite right. Uh, what was it? 5.25 is where I saw it. It's actually a little higher than 5.25. Cause we want this answer to be a little higher. It's actually 5.26, 5.27, 5.28, something like that. Right. And you just have to try them all in your calculator until you land right on it. Here. I'm going to say it's about 5.25 periods or 5.25 years. Now that's kind of unsatisfying to me, but you can get the answer that way. Right. And it's just like, okay, brute force your way to a solution in Excel. You can like goal seek, but if you have a financial calculator, you can just solve. So let's solve in our financial calculator. Let me pull up my little table here and we'll fill in the information that we've got. The number of periods is our thing that we're solving for. Our IY is 8%. Our PV value today, $50,000. We're going to invest today. There's no payments. There's no BGN. And, uh, our future value is $75,000. We put in 50 today to get 75 out in, uh, who knows how many years? 5.25, somewhere around there, a little higher. So let's punch in our numbers. I always clear, uh, memory to the best of my ability. And I go eight is my IY 50,000 negative is my PV. 75,000 positive is my F and that's everything. PMT is zero. I can, oops, no zero is PMT. I think I put it in 75 as PMT there by mistake. Uh, anyway, I think we're good now. I've, I've fixed my PMT. Now we want to compute the number of periods. So I'd say compute N and I get 5.268. So we knew we were close, but 5.268 is a more precise answer than 5.25. There we have it. We've solved 3, 4A. We did it the trial and error way and we got close and we could have got closer if we just stuck with it. Now we've got a much more precise answer using our financial calculator. I hope this video helped you. And if it did, I hope you'll give me the old thumbs up. Thanks for watching. Bye-bye.