Question

For both questions, please show what you typed into the TVM solver.

N:

I:

PV:

PMT:

FV:

Time of month: End or beginning

1. Rachel, who just turned 18, deposits a $15,000 gift into an interest-bearing account earning a 7.5% annual rate of interest. How much will she have in the account when she retires at age 60, assuming all interest is reinvested at the 7.5% rate? If Rachel decided she only needed $300,000 at retirement, could she retire at 59? Explain.

2. James deposited $800 at the end of the past 16 years to purchase his granddaughter, Kali, a car, James earned 8% interest compounded annually on his investment. If the car Kali chooses costs $22,999, would she have enough money in the account to purchase the vehicle? What would be the deficit or surplus?

Answer 1

Q1. Basically Rachel deposits 15000, so that is a cash outflow. therefore it should be input as a negative value in the PV. She deposited it at the completion of 18 years of age and we need to calculate the FV when she completed 60 years of age.

• N: 60-18 = 42
• I: 7.5
• PV: -15000
• PMT: 0
• FV:   $312,785.60 (computed)
• Time of month: End
• Algebraic calculation are as follows:
  • 
  • 
  • 
  • So the FV is  $3,12,785.60

Now as the FV is greater that 300000, we can check whether it is the same if she retires at 59, that is after 42 compounding periods,

• N: 59-18 = 41
• I: 7.5
• PV: -15000
• PMT: 0
• FV:   $2,90,963.35 (computed)
• Time of month: End
• Algebraic calculation are as follows:
  • 
  • 
  • 
  • So the FV is $2,90,963.35

FV is less than 300000 so she can't retire at the age of 59

Q2. James deposited $800 at the end of the past 16 years to purchase his granddaughter, Kali, a car, James earned 8% interest compounded annually on his investment. If the car Kali chooses costs $22,999, would she have enough money in the account to purchase the vehicle? What would be the deficit or surplus?

Basically James deposits 800 annually at the end of 16 years, so that is a cash outflow. therefore it should be input as a negative value in the PMT.

• N = 16
• I: 8
• PV: 0
• PMT: -800
• FV:    $24,259.43  (computed)
• Time of month: End
• Algebraic calculation are as follows:
  • 
  • 
  • 
  • So the FV is $24259.43
  • If the amount required to buy the car is 22999, then we have sufficient amount in the fund to buy the same.