Question

In: Finance

Find the present value of the following ordinaryannuities. (Notes: If you are using a financial...

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. $600 per year for 10 years at 14%.

    $   

  2. $300 per year for 5 years at 7%.

    $   

  3. $600 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 areannuities due.

    Present value of $600 per year for 10 years at 14%: $   

    Present value of $300 per year for 5 years at 7%: $   

    Present value of $600 per year for 5 years at 0%: $   

Solutions

Expert Solution

Calculation of the Present value of following annuities due -

(a) $600 per year for 10 years at 14%

Present value of annuity = Cash flow per period *PVIFA(14%,10years)

= 600*5.2161

= 3129.67

(b) $300 per year for 5 years at 7%.

Present value of annuity = Cash flow per period *PVIFA(7%,5years)

= 300*4.1002

= 1230.05

(c) $600 per year for 5 years at 0%

Present value of annuity = Cash flow per period *PVIFA(0%,5years)

= 600*5

= 3000

(d) Calculation of present value of parts a,b,c calculated assuming that payments are made at the beginning of each year

Present value of annuity due   = Present value of ordinary annuity * (1+i)

Present value of annuity due for part a = Present value of ordinary annuity * (1+i)

= 3129.67*(1+0.14)

= $ 3567.82

Present value of annuity due for part b = Present value of ordinary annuity * (1+i)

= 1230.04*(1+0.07)

= $ 1316.14

Present value of annuity due for part c = Present value of ordinary annuity * (1+i)

= 3000*(1+0.00)

= $ 3000

Note - PVIFA stands for Present value interest factor is the multiplier used to calculate at a specified discount rate the present value of an amount to be received in a future period.


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