Alright. So just like I promised, we're going to learn how to find the present value of annuities and the present value of lump sums using tables. Okay? Let's check it out. So instead of having those formulas that we've been working with so far and like I said, those formulas for annuities are beyond the scope of this course. Well, we're going to use tables that make it a lot easier to find the present value based on the interest rate and the number of periods. Remember, those were 2 of our variables that we used in finding present value. So those are going to be important when we use the tables. So in this course, we're generally going to be focused on present value, okay? We're going to be taking some future sums of money like those interest payments and those principal payments from bonds and we're going to find what those are worth today. Okay? And that's the key, we're finding those present values of those future sums of money. Specifically, like I said, we're finding what those future interest payments are. And like we saw in our previous example, the future interest payments, they form an annuity. Remember that an annuity is getting equal amounts of money, so the same amount of money each period, so in equal amount of time. So annual interest each year, you would be getting the same interest payment. Okay? That's what makes an annuity. And then there's also going to be principal payment at the very end. And that's going to be a lump sum. Right? There's just going to be the one principal payment at the end when they have to pay back the bond, they have to pay back the liability to the person who bought the bond. Well, that's going to be at the end as a lump sum. They're going to pay off the value of the bond. Okay? So we're going to be dealing with both, annuities and lump sums. So let's go ahead and see how we're going to use the tables to do our present values of lump sums and present value of annuity.

So remember when we use our formula for lump sums, where we had some future amount of money and we wanted to know what it is worth today. That was like the example where we were saving up for a European vacation and we wanted to have $12,000 in the future, well, how much did we need to invest in the bank today? Well, we can use a table to save us time rather than have that clunky formula with exponents and stuff. So remember, we had the future value, so our formula was:

P V = F V ∕ ( 1 + r ) nNotice how I highlighted the 1+r)n, because instead of doing the dividing by 1+r)n, we're going to have our future value and then we're going to multiply by the present value factor. And these present value factors, they come from the table, okay? So you'll see in the last page of this lesson, I've included the present value tables for lump sums and for annuities, okay? So we'll go over those before we're done here and before we get to the example. So notice, it's very simple. Instead of doing all of those calculations, what we have is the future value times the present value factor. And we're just going to get some number out of the table and multiply it by the future value and that's it. We found our present value.

Same thing with the annuities. Except in this case, we're going to use the annuity payment instead of the future value. So say you were going to get $10,000 a year for 5 years. Well, that would be the annuity payment is $10,000. We wouldn't add them all together and say $10,000 for 5 years, that's $50,000 total dollars. No, no, no. We're going to take the amount of each payment, which is $10,000, and that's going to be the amount in this formula, annuity payment and we're going to find the number in the table that we're going to multiply it by. Okay? So let's pause here and then we're going to go to the tables and we're going to do a quick explanation of how to read the tables and we'll come back to the example. So flip over to the other page where you've got the tables listed. Alright? Let's do that.