Find the present value of the following ordinary annuities R

Find the present value of the following ordinary annuities. Round your answers to the nearest cent. (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 FV, and find the FV of the annuity due.)

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

$400 per year for 5 years at 5%.
$   

$800 per year for 5 years at 0%.
$  

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

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

$400 per year for 5 years at 5%.
$   

$800 per year for 5 years at 0%.
$  

Solution

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

Present value = 800 * Cumulative P.V. factor for 10 Years @ 10 %

= 800 * 6.1446

   = $ 4915.68

Future value = Present value * ( 1 + r)^N  

= 4915.68 * ( 1 + 0.10)¹⁰

= 4915.68 * 2.5937

= $ 12749.80

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

Present value = 400 * Cumulative P.V. factor for 5 Years @ 5 %

= 400 * 4.3295

   = $ 1731.80

Future value = Present value * ( 1 + r)^N  

= 1731.80 * ( 1 + 0.05)⁵

= 1731.80 * (1.05)⁵

   = 1731.80 * 1.27628

= $ 2210.26

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

Both present value = future value = 800 * 5 = $ 4000

Now, assuming that payments are made at the beginning of each year; that is, they are annuities due. Decrease n (Time period) by 1 year.

4) $800 per year for 10 years at 10%.

Present value = 800 + 800 * Cumulative P.V. factor for 9 Years @ 10 %

= 800 + 800 * 5.7590

   = 800 + 4607.20

   = $ 5407.20

Future value = Present value * ( 1 + r)^N  

= 4607.20 * ( 1 + 0.10)¹⁰

= 4607.20 * 2.5937

= $ 11949.69

5) $400 per year for 5 years at 5%.

Present value = 400 + 400 * Cumulative P.V. factor for 4 Years @ 5 %

= 400 + 400 * 3.546

   = 400 + 1418.40

   = $ 1818.40

Future value = 1418.40 * ( 1 + r)^N  

= 1418.40 * ( 1 + 0.05)⁵

= 1418.40 * (1.05)⁵

= 1418.40 * 1.2763

= $ 1810.30

6) $800 per year for 5 years at 0%.

Present value = future value = 800 * 5 = $ 4000