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Chris Jones wishes to have $200,000 in a retirement fund 30 years from now. He can...

Chris Jones wishes to have $200,000 in a retirement fund 30 years from now. He can create the retirement fund by making a single lump-sum deposit today. Use next table to solve the following problems.

  1. If he can earn 8 percent on his investments, how much must Chris deposit today to create the retirement fund? Round PV-factor to three decimal places. Round your answer to the nearest cent.
    Calculate your answer based on the PV-factor.

    $  


    Calculate your answer based on the financial calculator.

    $  


  3. If he can earn only 6 percent on his investments? Round PV-factor to three decimal places. Round your answer to the nearest cent.
    Calculate your answer based on the PV-factor.

    $  


    Calculate your answer based on the financial calculator.

    $  


  5. If upon retirement in 30 years Chris plans to invest the $200,000 in a fund that earns 6%, what is the maximum annual withdrawal he can make over the following 20 years? Round the answer to the nearest cent. Round PVA-factor to three decimal places.
    Calculate your answer based on the PVA-factor.

    $  


    Calculate your answer based on the financial calculator.

    $  


  7. How much would Chris need to have on deposit at retirement to annually withdraw $35,000 over the 20 years if the retirement fund earns 6%? Round the answer to the nearest cent. Round PVA-factor to three decimal places.
    Calculate your answer based on the PVA-factor.

    $  


    Calculate your answer based on the financial calculator.

    $  


  9. To achieve his annual withdrawal goal of $35,000 calculated in part c, how much more than the amount calculated in part a must Chris deposit today in an investment earning 6% annual interest? Round PVA-factor to three decimal places. Round your answer to the nearest cent. If an amount is zero, enter "0".

    $  

Solutions

Expert Solution

PV table:

a. FV = $200,000

Time till retirement = 30 years

r = 8 percent on his investments

  • We need to calculate the PV that will result in FV of 200000 in 30 years at 8% compounding
  • required PV factor is 0.09934
  • Formula for required FV:
    • or

b. Calculate your answer based on the financial calculator.

  • Inputs for Financial calculator:
    • PMT=0
    • I/Y = 0.08
    • FV = 200000
    • T=30
    • CPT PV
    • In the financial calculator the PV value will be negative because it is an outflow which will result in an outflow of 200000 @ 8% after 30 years

FV = $200,000

Time till retirement = 30 years

r = 6 percent on his investments

c. Answer based on the PV-factor.

  • required PV factor is 0.1741
  • Formula for required FV:
    • or

d. Answer based on the financial calculator.

  • Inputs for Financial calculator:
    • PMT=0
    • I/Y = 0.06
    • FV = 200000
    • T=30
    • CPT PV
    • In the financial calculator the PV value will be negative because it is an outflow which will result in an outflow of 200000 @ 6% after 30 years

e. answer based on the PVA-factor.

PV = $200,000

Time till last withdrawal = 20 years

r = 6 percent on his investments

  • We need to calculate the PMT that can come from a PV of 200000 and FV = 0 in 20 years at 6% compounding
  • required PVA factor is 11.4699
  • Formula for required FV:
    • or

f. answer based on the financial calculator.

  • Inputs for Financial calculator:
    • I/Y = 0.06
    • PV = 200000
    • T=20
    • FV=0
    • CPT PMT
    • In the financial calculator the PMT value will be negative because it is an outflow or a withdrawal which will result from outflow of 200000 @ 6% during each of the 20 years

g. answer based on the PVA-factor.

PMT =35000  

Time till last withdrawal = 20 years

r = 6 percent on his investments

  • We need to calculate the PV that can come result in a PMT of 35000 and FV = 0 in 20 years at 6% compounding
  • required PVA factor is 11.4699
  • Formula for required FV:
    • or

h. answer based on the financial calculator.

  • Inputs for Financial calculator:
    • I/Y = 0.06
    • T=20
    • FV=0
    • PMT = -35000
    • CPT PV
    • In the financial calculator the PMT value will be negative because it is an outflow or a withdrawal of 35000 @ 6% during each of the 20 years

To achieve his annual withdrawal goal of $35,000 calculated in part c, how much more than the amount calculated in part a must Chris deposit today in an investment earning 6% annual interest? Round PVA-factor to three decimal places. Round your answer to the nearest cent. If an amount is zero, enter "0".

Total FV required = $401446.50

Of this 200000 will be achieved as per part a, and for the remaining 201446.50 will be calculated as follows

Time till retirement = 30 years

r = 6 percent on his investments

  • We need to calculate the PV that will result in FV of 201446.50 in 30 years at 6% compounding
  • required PV factor is 0.1741
  • Formula for required FV:
  • or

jeff jeffy answered 7 months ago
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