Question

Use what you have learned about the time value of money to analyze each of the following decisions: Decision #1: Which set of Cash Flows is worth more now? Assume that your grandmother wants to give you generous gift. She wants you to choose which one of the following sets of cash flows you would like to receive:

Option A: Receive a one-time gift of $10,000 today.

Option B: Receive a $1600 gift each year for the next 10 years. The first $1600 would be received 1 year from today.

Option C: Receive a one-time gift of $20,000 10 years from today.

Compute the Present Value of each of these options if you expect the interest rate to be 3% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

Compute the Present Value of each of these options if you expect the interest rate to be 6% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

Compute the Present Value of each of these options if you expect to be able to earn 10% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

Decision #2 begins at the top of page 2!

Decision #2: Planning for Retirement Todd and Jessalyn are 25, newly married, and ready to embark on the journey of life. They both plan to retire 45 years from today. Because their budget seems tight right now, they had been thinking that they would wait at least 10 years and then start investing $2400 per year to prepare for retirement. Jessalyn just told Todd, though, that she had heard that they would actually have more money the day they retire if they put $2400 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments - than they would have if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do).

Please help Todd and Jessalyn make an informed decision: Assume that all payments are made at the end of a year, and that the rate of return on all yearly investments will be 7.2% annually.

a) How much money will Todd and Jessalyn have in 45 years if they do nothing for the next 10 years, then puts $2400 per year away for the remaining 35 years?

b) How much money will Todd and Jessalyn have in 10 years if they put $2400 per year away for the next 10 years?

b2) How much will the amount you just computed grow to if it remains invested for the remaining 35 years, but without any additional yearly deposits being made?

c) How much money will Todd and Jessalyn have in 45 years if they put $2400 per year away for each of the next 45 years?

d) How much money will Todd and Jessalyn have in 45 years if they put away $200 per MONTH at the end of each month for the next 45 years? (Remember to adjust the 9% annual rate to a Rate per month!) (Round this rate per month to 5 places past the decimal) example of rounding: .062134 = .06213 or 6.213%

e) If Todd and Jessalyn wait 25 years (after the kids are raised!) before they put anything away for retirement, how much will they have to put away at the end of each year for 20 years in order to have $8,000,000 saved up on the first day of their retirement 45 years from today?

Answer 1

As per rules I am answering the first 4 subparts of the question

1: Present values as follows

Option A: 10000

Option B :

PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

= 1600*(1-1/(1+0.03)^10)/0.03

=13648.32

Option C:

Present value = Future value/(1+Rate)^number of periods

= 20000/1.03^10

=14881.88

Financial theory supports choosing Option C since it has highest present value

2: Present values as follows

Option A: 10000

Option B :

PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

= 1600*(1-1/(1+0.06)^10)/0.06

=11776.14

Option C:

Present value = Future value/(1+Rate)^number of periods

= 20000/1.06^10

=11167.9

Financial theory supports choosing Option B since it has highest present value

3: Present values as follows

Option A: 10000

Option B :

PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

= 1600*(1-1/(1+0.1)^10)/0.1

=9831.31

Option C:

Present value = Future value/(1+Rate)^number of periods

= 20000/1.1^10

=7710.87

Financial theory supports choosing Option A since it has highest present value

4: Future Value of annuity = A*((1+rate)^number of periods-1)/rate

= 2400*((1+0.072)^35-1)/0.072

=346590.2

They will have 346590.2 after 45 years.