Question

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.

   $  

2. 
   
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.

   $  

4. 
   
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.

   $  

6. 
   
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.

   $  

8. 
   
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".

   $  

Answer 1

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
• 
•