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 |
|
Future Value of 1 |
1.99900 |
2.15892 |
2.33164 |
Present Value of 1 |
.50025 |
.46319 |
.42888 |
Future Value of Ordinary Annuity of 1 |
12.48756 |
14.48656 |
16.64549 |
Present Value of Ordinary Annuity of 1 |
6.24689 |
6.71008 |
7.13896 |
Present Value of an Annuity Due of 1 |
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.
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
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