Question

Find the present value of the following ordinary annuities. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press PV, and find the PV of the annuity due.) Do not round intermediate calculations. Round your answers to the nearest cent.

1. $800 per year for 10 years at 6%.

   $ ---------

2. $400 per year for 5 years at 3%.

   $ -----------

3. $800 per year for 5 years at 0%.

   $ ----------

4. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

   Present value of $800 per year for 10 years at 6%: $ --------

   Present value of $400 per year for 5 years at 3%: $ ------------

   Present value of $800 per year for 5 years at 0%: $ ---------

Answer 1

We can use the financial calculator and put in these values,

a) pmt = $800, time = 10, i = 6%, CPT PV = $5,888.07

We can also use excel,

pmt	800
time	10
rate	6%
Pv	5888.07	(=PV(6%,10,-800,0,0)

b)

pmt = $400, time = 5, i = 3%, CPT PV = $1,831.88

We can also use excel,

pmt	400
time	5
rate	3%
Pv	1831.88	(=PV(3%,5,-400,0,0)

c)

pmt = $800, time = 5, i = 0%, CPT PV = $4,000

We can also use excel,

pmt	800
time	5
rate	0%
Pv	$4,000	(=PV(0%,5,-800,0,0)

d) If payments are made in the beginning, we will change the last value in the excel formula from 0 to 1.

i)

pmt	800
time	10
rate	6%
Pv	6241.35	(=PV(6%,10,-800,0,1)

PV = $6,241.35

ii)

pmt	400
time	5
rate	3%
Pv	1886.84	(=PV(3%,5,-400,0,1)

PV = $1,886.84

iii)

pmt	800
time	5
rate	0%
Pv	4000.00	(=PV(0%,5,-800,0,1)

PV = $4,000

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