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1Your family owns a velociraptor skeleton that is currently valued at $86.7 thousand. Your grandfather, being an avid fossil collector, bought it 50 years ago for $24.8 thousand. If the skeleton keeps appreciating at the same average annual rate, what would be its value 25 years from now?

2You would like to establish a trust fund that would pay annual payments to your heirs of $98 thousand a year forever. You expect the trust fund to earn an average return of 8.84 percent. How much do you need to deposit into this trust fund today to achieve your goal?

3You are thinking of investing in a project that will pay you $100,000 7 years from now, and another $100,000 10 years from now. You think the right discount rate for the project is 6.9%. What is the maximum you should be willing to pay for this investment?

4A firm recently purchased a new facility costing $962 thousand. The firm financed this purchase with an amortized loan at an interest rate of 9.7 percent APR, with monthly payments of $16.1 thousand. How long will it take to pay off this loan? (Enter answer in months, accurate to two decimal places.)

5An investment is expected to produce $2,370 at the end of each year for the next 10 years. Other investments of similar riskiness available to you are yielding 8.4 percent return. What is the maximum you should be willing to pay for this investment?

6You are not thrilled about spending your entire life working. So, you have decided that you will save $6 thousand a year, starting at the end of this year, and retire as soon as you can accumulate $1 million. If you can earn an average of 8.47 percent on your savings, how many years will pass before you get to retire?

7How much money must you invest today, at 7.7 percent fixed annual interest rate, in order to have 10 thousand in 13 years?

8You have $1,895 today, and want to double your money in 19 years. What interest rate must you earn to achieve your goal?

9The house you want to buy costs $260 thousand. You plan to make a cash down payment of 10 percent, and borrow the rest in a 30 year mortgage at 4.8 percent APR. What will be the amount of your monthly mortgage payment?

10You estimate that you will need $771 thousand in 30 years to buy some cybernetic body enhancements, including infrared vision, retractable claws, and expanded brain storage capacity. To achieve your financial goal, you want to make three equal-sized deposits into an account paying a fixed annual rate of 8.82%. The first deposit will be made right now, the second 10 years from now, and the third 20 years from now. What is the size of each deposit you need to make in order to partake of future cybernetic goodness? (Hint: draw this out on a timeline.)

Explanation / Answer

Solution 1:

Given that Future value, FV = $867,000, Present Value, PV = $248,000 and Number of years, n = 50

First, we calculate the annual rate, I.

FV = PV (1 + I)^n

$867,000 = $248,000 (1 + I)^50

$867,000/$248,000 = (1 + I)^50

3.495968 = (1 + I)^50

(3.495968)^(1/50) = 1 + I

1 + I = 1.02535

I = 0.02535

I = 2.535%

Now, we calculate the value 25 years from now.

FV = PV (1 + I)^n

FV = $867,000 (1.02535)^25

FV = $867,000 (1.869751)

FV = $1,621,073.87

Hence, the value 25 years from now is $1,621,073.87

Solution 2:

Given that Annual payment, A = $98,000 and Average return, I = 8.84%

Since the payment is made forever, it is perpetuity.

Present value of perpetuity, PV

PV = A/I

PV = $98,000/0.0884

PV = $1,108,597.29

Hence, you need $1,108,597.29 to deposit into this trust fund today to achieve your goal.

Solution 3:

Given that Cash flow at 7 years, CF7 = $100,000,

Cash flow at 10 years, CF10 = $100,000 and

Discount rate, I = 6.9%

The maximum amount paid for the investment, PV

PV = CF7/(1+I)^n + CF10/ (1 + I)^n

PV = $100,000/1.069^7 + $100,000/1.069^10

PV = $62,683.908 + $51,312.473

PV = $113,996.38

Hence, the maximum amount should be willing to pay for this investment is $113,996.38.

Solution 4:

Given that Monthly payments, PMT = $161,000,

Interest rate, I = 9.7%

Present value of loan, PV = $962,000

PV = PMT (PVIFA @ I, n)

$962,000 = $161,000 (PVIFA @ 9.7%, n)

$962,000/$161,000 = PVIFA @ 9.7%, n

5.975155 = PVIFA @ 9.7%, n

Using Present value interest factor tables,

PVIFA @ 9.7%, 9 = 5.82834

PVIFA @ 9.7%, 10 = 6.22456

Using Interpolation,

9 + (6.22456 – 5.975155)/ (6.22456 – 5.82834) * (10 – 9)

9 + 0.249406/0.396218

9 + 0.3598

9.3598 years

For monthly, we multiply by 12

n = 9.3598 x 12

n = 112.32 months

Hence, it will take 112.32 months to pay off the loan.

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