I have been stuck for over an hour with the following problem. In my textbook the following is written:
"Suppose, for example, that Polany Manufacturing Company enters into a long-term lease July 1 for a machine. The lease terms call for an annual payment of $8,000 for six years, which approximates the useful life of the machine. At the end of the lease period, the title to the machine passes to Polany. This lease is clearly a capital lease and should be recorded as an asset and a liablity.
Present value techniques can be used to place a value on the asset and on the corresponding liability in a capital lease. Suppose Polany's interest cost on the unpaid part of its obligation is 8 percent. Using the factor for 8 percent and six periods in Table 13-2 in the appendix on present values tables, we can compute the present value of the lease payments as follows:
Periodic Payment x Factor = Present Value
$$\$8{,}000 \cdot 4.623 = \$36{,}984$$
**My question is how did they come on the 4.623 interest factor amount? **
This is the table that goes with it
It's the sum of the present values of payments of $1$ at $8%$ over $6$ periods so:
$\dfrac{1}{(1.08)^{1}} + \dfrac{1}{(1.08)^{2}} + ... +\dfrac{1}{(1.08)^{6}}=4.623$
It probably makes more sense for you to just calculate the present value of the payements themselves i.e.:
$\dfrac{8 000}{(1.08)^{1}} + \dfrac{8 000}{(1.08)^{2}} + ... +\dfrac{8 000}{(1.08)^{6}}=36 984$
but notice that if you take out $8 000$ as a factor (from both sides) you get:
$\left(\dfrac{1}{(1.08)^{1}} + \dfrac{1}{(1.08)^{2}} + ... +\dfrac{1}{(1.08)^{6}}\right)\times8000=4.623\times8 000=36 984$