Question

1. Kate and Ken are in the market for a vacation place. They find a small but pleasant condo in Orlando listed at $478,000. They decide that now is not the right time to buy and that they will wait five years. The condos in Orlando appreciated each year at 2.5%, and they want to know what a similar condo will sell for in five years. Please help them and find it out. (3 points)

2. Terry would like to make a single investment and have $1 million at the time of his retirement in 20 years. He has found a mutual fund that will earn 3.6 percent annually. How much will Terry have to invest today? What if Terry learned how to earn a 7.5 percent annual return, how much would he have to invest today? (3 points)

3. You are offered $3,400 today, $8,000 in 10 years, or $20,000 in 20 years. Assuming that you can earn 9 percent on your money, which should you choose? (4 points)

4. Wilson needs to borrow $12,500 today for his tuition bill. He agrees to pay back the loan in a lump-sum payment five years from now, after he is out of college. He bank states that the payment will need to be $16,450. If Wilson borrows the $12,500 from the bank, what interest rate is he paying on his loan? (3 points)

5. You are the planning commissioner for T-Town, a growing city in the Southeast. The city council has estimated that the city’s population will increase very rapidly over the next twenty years, reaching an estimated 258,000. Today, the population is 132,500. What is the project growth rate of this city? (3 points)

6. Which of the following will result in a future value of greater than $100? (4 points)

1. PV = $50, I = annual interest rate of 10%, and n = 8 years
2. PV = $75, I = annual interest rate of 12%, and n = 3 years
3. PV = $90, I = annual interest rate of 14%, and n = 1 year

7. Tom asked Sarah to marry him, and she has accepted under one condition. Tom must buy a $250,000 house. Tom currently has $175,640 that he may invest. He has found a mutual fund that pays 5.4% annual interest in which he will place the money. How long will it take Tom to marry Sarah? (3 points)

8. Approximately how long will it take to double your money if you get 8.75% annual return on your investment? Verify the approximate doubling period with your financial calculator. (4 points)

9. William, age 20, wants to be able to buy a really cool new car when he turns 26. His really cool car costs $25,000 today, and its cost is expected to increase 3 percent annually. William wants to make one deposit today into an account paying 6.5 percent annually in order to buy his car in 6 year. How much will William’s car cost, and how much does William have to save today in order to buy this car at age 26. (4 points)

10. Sunny and Emily put $3,000 into a college fund every year for their son, James, on his birthday, with the first deposit one year from his birth (at his very first birthday). The college fund has a guaranteed annual growth or interest rate of 4.2%. At his eighteenth birthday, they will pay the last $3,000 into the fund. How much will be in the college fund for James immediately following this last payment? (4 points)

            

11. Patman dealership is offering you a great deal on a “preowned” car. He says, “For only six annual end-of-the year payments of $3,940, the beautiful 2019 Honda Civic can be yours.” If you can borrow money a 5%, what is the price of the car today? If you are to make the payment at the beginning of the year, what is the price of the car today? (4 points)

Part II (11 points in total)

A group of college students won a record Powerball jackpot of $423 million. The group had 2 choices:

      A) Receive 30 beginning of the year payments of 14.1 million each

      B) Receive a lump sum payment today of $211.5 million immediately

1. Draw the time lines for the two choices.
2. Find the FV (at the end of year 30) of the two choices assuming interest rate is 11%? Which choice should the group select?
3. Find the PV of the two choices assuming interest rate is 11%. Which choice should the group select?
4. Find the FV (at the end of year 30) for the two choices assuming interest is 4%. Which choice should the group select?
5. Find the PV of the two choices assuming interest rate is 4%. Which choice should the group select?

Answer 1

Kate and ken

PV(Present Value)=478000,n=number of years=5,r=interest rate=2.5%,FV(Future Value)=?

FV=PV(1+r^n)

=478000(1+0.025)^5

478000*1.131

540813.1257

Terry

n=20,Fv=1mn=1000000,r=3.6%,PV=?

Pv=FV/(1+r^n)

1000000/(1.036^20)

=$4,92,950.80351

r=7.5%

PV=1000000/(1.075^20)

=$235413.21

Today 3400, 8000 in 10 years and 20000 in 20 years , r=0.09

PV=8000?(1.09^10)

3379.2

PV=20000/(1.09^20)

3568.6

hence 20000 in 20 years, has to be selected as its value today is 3568.6.

Wilson

PV=12500,n=5,FV=16450,r=?

FV=PV(1+r^n)

16450=12500(1+r)^5

1.36=(1+r)^5

5th root of 1.36=1+r

5.831=1+r

r=4.831

Interest loan he is paying is 4.8%

T-Town

Fv=258000,Pv=132500,n=20,r=?

258000=132500(1+r^20)

1.947=(1+r^20)

20th root of 1.947=1+r

27.91=1+r

r=26.91%.

Fv greater than 100

Fv1=PV(1+r^n)

=50(1+0.1^8)

$107.18

Fv2=75(1+0.12)^3

$105.37

Fv3=90(1+0.14)^1

$102.6 So all three value is greater than $100.

Tom marry Sarah

Pv=Fv(1+r)^n

175640/250000=1.054^n

0.70256=1.054^n

n log(1.054)=log(0.70256)

n=6.7 years.

Doubling Period

r=8.75%,FV=2PV

PV=2PV(1+0.0875)^n

0.5=1.0875^n

log(0.5)/log(1.0875)=n

n=8.26years.

Sunny and Emily

n=18,r=4.2%,A=3000

Present value of annuity problem.

PV=A[(1-(1+r)^-n)/r]

3000[1-(1+0.042)^-18/0.042]

3000[1-0.47685/0.042]

=$37,367

Patman Dealership

A=3940,r=0.05,n=6,

Present value of annuity due formula since its at the beginning

p[1-(1+r)^-n/r](1+r)

3940[1-(1+0.05)^-6/0.05]/(1+0.05)

3940[1-0.7462/0.05](1.05)

=3940*5.076*1.05

=$20999.412