Question

4) Determine the present value of $35,000 to be received at the end of each of five years, using an interest rate of 5%, compounded annually, as follows:

a) By successive computations, using the Present Value of $1 table below. You must show your work.

b) By a single computation using the Present Value of an Annuity of $1 table below. You must show your work.

Note: The two answers will not come out exactly the same, but should be close (within 1/2 percent).

Answer 1

(a)-Present Value of the payments by successive computations, using the Present Value Factor

Year	Annual cash flows ($)	Present Value Factor (PVF) at 5.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	35,000	0.9523810	33,333.33
2	35,000	0.9070295	31,746.03
3	35,000	0.8638376	30,234.32
4	35,000	0.8227025	28,794.59
5	35,000	0.7835262	27,423.42
TOTAL	4.3294767	151,531.68

The Present Value will be $151,531.68

(b)-Present Value of the payments by single computation using the Present Value of an Annuity

Present Value = Annual payments x Present Value annuity factor at 5.00% for 5 Years

= Annual payment x (PVIFA 5.00%, 5 Years)

= $35,000 x 4.3294767

= $151,531.68

The Present Value will be $151,531.68

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.