Question

1.

eBook Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent. $200 per year for 14 years at 8%. $   $100 per year for 7 years at 4%. $   $400 per year for 7 years at 0%. $   Rework previous parts assuming they are annuities due. Present value of $200 per year for 14 years at 8%: $   Present value of $100 per year for 7 years at 4%: $   Present value of $400 per year for 7 years at 0%: $   2 Find the present values of the following cash flow streams at a 6% discount rate. Do not round intermediate calculations. Round your answers to the nearest cent. 0 1 2 3 4 5 Stream A $0 $150 $400 $400 $400 $300 Stream B $0 $300 $400 $400 $400 $150 Stream A: $   Stream B: $   What are the PVs of the streams at a 0% discount rate? Round your answers to the nearest dollar. Stream A: $   Stream B: $
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Answer 1

Answer to Question 1:

Part a:

Annual Payment = $200
Time Period = 14 years
Interest Rate = 8%

Present Value = $200/1.08 + $200/1.08^2 + … + $200/1.08^13 + $200/1.08^14
Present Value = $200 * (1 - (1/1.08)^14) / 0.08
Present Value = $200 * 8.244237
Present Value = $1,648.85

Part b:

Annual Payment = $100
Time Period = 7 years
Interest Rate = 4%

Present Value = $100/1.04 + $100/1.04^2 + … + $100/1.04^6 + $100/1.04^7
Present Value = $100 * (1 - (1/1.04)^7) / 0.04
Present Value = $100 * 6.002055
Present Value = $600.21

Part c:

Annual Payment = $400
Time Period = 7 years
Interest Rate = 0%

Present Value = $400 + $400 + $400 + $400 + $400 + $400 + $400
Present Value = $400 * 7
Present Value = $2,800.00

Part d:

Annuity 1:

Annual Payment = $200
Time Period = 14 years
Interest Rate = 8%

Present Value = $200 + $200/1.08 + $200/1.08^2 + … + $200/1.08^12 + $200/1.08^13
Present Value = $200 * 1.08 * (1 - (1/1.08)^14) / 0.08
Present Value = $200 * 8.903776
Present Value = $1,780.76

Annuity 2:

Annual Payment = $100
Time Period = 7 years
Interest Rate = 4%

Present Value = $100 + $100/1.04 + $100/1.04^2 + … + $100/1.04^5 + $100/1.04^6
Present Value = $100 * 1.04 * (1 - (1/1.04)^7) / 0.04
Present Value = $100 * 6.242137
Present Value = $624.21

Annuity 3:

Annual Payment = $400
Time Period = 7 years
Interest Rate = 0%

Present Value = $400 + $400 + $400 + $400 + $400 + $400 + $400
Present Value = $400 * 7
Present Value = $2,800.00