Present value of an ordinary annuity and annuity due Jill Mo

Present value of an ordinary annuity and annuity due.
Jill Morris is presently leasing a small business computer from Eller Office Equipment Company. The lease requires 10 annual payments of $6,000 at the end of each year and provides the lessor (Eller) with an 8% return on its investment. You may use the following 8% interest factors:

9 Periods

10 Periods

11 Periods

1.99900

2.15892

2.33164

.50025

.46319

.42888

12.48756

14.48656

16.64549

6.24689

6.71008

7.13896

6.74664

7.24689

7.71008

Instructions
(a) Assuming the computer has a ten-year life and will have no salvage value at the expiration of the lease, what was the original cost of the computer to Eller? SHOW YOUR WORK.

(b) What amount would each payment be if the ten annual payments are to be made at the beginning of each period? SHOW YOUR WORK.

Solution

Requirement (a) - Original cost of the computer to Eller

Original cost of the computer to Eller = Present Value of an ordinary annuity payments of $6,000 at 8% for 10 Years

= Annual Payments x Present Value of Factor of an ordinary Annuity of 1       

= $6,000 x 6.71008

= $40,260

Requirement (b) – Amount of each 10 annual payments

Annual Payments = Original cost of the compute / Present Value of an Annuity Due of 1    

= $40,260 / 7.24689

= $5,555