First, as discussed above, you need to know the amount and timing of payments to be made or expected to be received. In the first example, you expect $11,000 five years from now. In the second, you expect $200 in year 1, $200 in year 2, $200 in year 3, $200 in year 4, and $10,200 in year 5.

Once you’ve determined this, you have a couple of vital pieces of information:

You know whether you’re looking at a lump sum, an annuity (a stream of payments), or both. In the first example, it’s a lump sum. In the second, it’s an annuity of $200, and a lump sum of $10,000 (because the $200 in year 5 belongs to the annuity of $200, not to the lump sum of the principal).

This tells you what present value tables to use. You use the Present Value of $1 (Present Value of a Single Sum) table to value the lump sums. You use the Present Value of an Ordinary Annuity to value streams of payments. So in the second example, you’d use the PV of $1 table to get the present value of the $10,000 lump sum, and you’d use the PV of an Ordinary Annuity table to get the present value of the five $200 payments.

Before you can use the tables, though, there is one more step. You need to find n, and i. * n is the number of interest compounding periods involved. * If you are looking at the PV of a lump sum, n = the number of years before the sum will be paid. In the first example, n = 5. * It is more complicated if you are looking at an annuity. If the annuity stream (interest, for purposes of Chapter 14) is paid annually, n = number of years during which the sum will be paid. In the second example, if we assume annual interest payments, n = 5. BUT if your interest is paid some other way that annually – semi-annually, or quarterly, for example, you need to determine how many interest payments there will be. For the second example, instead of assuming annual payments, assume that interest gets paid semi-annually. If it’s a five year term, how many interest payments are we talking about then? 5 years x 2 payments per year = 10. So n = 10 in this situation. Likewise, if we assume quarterly payments, then 5 years x 4 payments per year = 20, and n = 20. * i is the effective interest rate. As with n we need to keep the number of payments per year in mind. Let’s assume a 10% rate. * If interest is paid annually, i = 10%. * If interest is paid semi-annually, i is 10% ÷ 2 = 5%. Every interest payment is 5% of the principal. You’re still getting 10% every year, but because you get paid twice, each payment is only half of what it would be if you got paid annually. * If the interest is paid quarterly, i = 10% ÷ 4 = 2.5%. * You need to determine the amount of each interest payment, too. * If it’s paid annually, and the rate is 10%, then each payment is $10,000 x 10% = $1,000. * If it’s paid semiannually, the rate of each payment is 5%, so the amount of the payment would be $10,000 x 5% = $500. * If it’s paid quarterly, the rate of each payment is 2.5%, so the amount of the payment would be $10,000 x 2.5% = $250. You can see that no matter how we cut it up, you’re still getting $1,000 per year, and the annual interest rate is still 10%.

Now that you know 1. the amount of any lump sum to be paid or collected in the future, 2. the amount of each interest payment (which may not be the same as the total annual interest payment!), 3. n, the number of interest compounding periods, and 4. i, the effective interest rate
You are ready to use the tables.

For your lump sum 1. Look at the Present Value of $1 table. Locate the factor that corresponds to n (rows) and i (columns). 2. Multiply that factor by the amount of the lump sum. 3. This is the present value of that lump sum. 4. If you have a series of interest payments, go to the Annuity, below. Otherwise, you’re done – you have the present value of the debt or investment.

For the annuity 1. Look at the Present Value of an Ordinary Annuity table. Locate the factor that corresponds to n (rows) and i (columns). 2. Multiply that factor by the amount of the interest payment (as calculated above, where you took the number of payments per year into consideration). 3. This is the present value of that series of interest payments. 4. Add that to the present value of the lump sum, from step 3, above, to get the present value of the entire debt or investment.