Question

5. 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.

   a   $200 per year for 10 years at 14%.

   b   $100 per year for 5 years at 7%.

   c   $200 per year for 5 years at 0%.

   d   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 $200 per year for 10 years at 14%: $   
Present value of $100 per year for 5 years at 7%: $   
Present value of $200 per year for 5 years at 0%: $

Answer 1

Answer a.

Annual Payment = $200
Time Period = 10 years
Interest Rate = 14%

Present Value = $200/1.14 + $200/1.14^2 + … + $200/1.14^9 + $200/1.14^10
Present Value = $200 * (1 - (1/1.14)^10) / 0.14
Present Value = $200 * 5.216116
Present Value = $1,043.22

Answer b.

Annual Payment = $100
Time Period = 5 years
Interest Rate = 7%

Present Value = $100/1.07 + $100/1.07^2 + $100/1.07^3 + $100/1.07^4 + $100/1.07^5
Present Value = $100 * (1 - (1/1.07)^5) / 0.07
Present Value = $100 * 4.100197
Present Value = $410.02

Answer c.

Annual Payment = $200
Time Period = 5 years
Interest Rate = 0%

Present Value = $200 + $200 + $200 + $200 + $200
Present Value = $200 * 5
Present Value = $1,000

Answer d-1.

Annual Payment = $200
Time Period = 10 years
Interest Rate = 14%

Present Value = $200 + $200/1.14 + … + $200/1.14^8 + $200/1.14^9
Present Value = $200 * 1.14 * (1 - (1/1.14)^10) / 0.14
Present Value = $200 * 5.946372
Present Value = $1,189.27

Answer d-2.

Annual Payment = $100
Time Period = 5 years
Interest Rate = 7%

Present Value = $100 + $100/1.07 + $100/1.07^2 + $100/1.07^3 + $100/1.07^4
Present Value = $100 * 1.07 * (1 - (1/1.07)^5) / 0.07
Present Value = $100 * 4.387211
Present Value = $438.72

Answer d-3.

Annual Payment = $200
Time Period = 5 years
Interest Rate = 0%

Present Value = $200 + $200 + $200 + $200 + $200
Present Value = $200 * 5
Present Value = $1,000