Question

Calculate the present value of the following:

a-1. Annual payment of $775 for 10 years at 4% interest. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present Value:

a-2. Annual payment of $575 for 15 years at 4% interest. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present Value:

a-3. Which option would you prefer?

• $775 a year for 10 years

• $575 a year for 15 years

b-1. Annual payment of $775 for 10 years at 16% interest. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present Value:

b-2. Annual payment of $575 for 15 years at 16% interest. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present Value:

b-3. Which option would you prefer?

• $775 a year for 10 years

• $575 a year for 15 years

Answer 1

Answer a.

Option 1:

Annual Payment = $775
Number of Payments = 10 years
Interest Rate = 4%

Present Value = $775/1.04 + $775/1.04^2 + … + $775/1.04^9 + $775/1.04^10
Present Value = $775 * (1 - (1/1.04)^10) / 0.04
Present Value = $775 * 8.110896
Present Value = $6,285.94

Option 2:

Annual Payment = $575
Number of Payments = 15 years
Interest Rate = 4%

Present Value = $575/1.04 + $575/1.04^2 + … + $575/1.04^14 + $575/1.04^15
Present Value = $575 * (1 - (1/1.04)^15) / 0.04
Present Value = $575 * 11.118387
Present Value = $6,393.07

You should prefer $575 a year for 15 years as its present value is higher.

Answer b.

Option 1:

Annual Payment = $775
Number of Payments = 10 years
Interest Rate = 16%

Present Value = $775/1.16 + $775/1.16^2 + … + $775/1.16^9 + $775/1.16^10
Present Value = $775 * (1 - (1/1.16)^10) / 0.16
Present Value = $775 * 4.833227
Present Value = $3,745.75

Option 2:

Annual Payment = $575
Number of Payments = 15 years
Interest Rate = 16%

Present Value = $575/1.16 + $575/1.16^2 + … + $575/1.16^14 + $575/1.16^15
Present Value = $575 * (1 - (1/1.16)^15) / 0.16
Present Value = $575 * 5.575456
Present Value = $3,205.89

You should prefer $775 a year for 10 years as its present value is higher.