Question

Please answer the following questions and show the work.

Calculating Interest rates:
In January 2007, the average house price in the US was $314,600. In January 2000, the average price was $200,300.
What was the annual increase in selling price?

Calculating the Number of Periods:
You’re trying to save to buy a new $170,000 Ferrari, You have $40,000 today that can be invested at your bank. The bank pays 5.3 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

Calculating Present Values:
You have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you’re around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 10 percent?

Calculating Future Values:
Your coin collection contains fifty 1952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2057, assuming they appreciate at a 4.5 percent annual rate?

Present and Future Values:
The present value of the following cash flow stream is $6,550 when discounted at 10 percent annually. What is the value of the missing cash flow?

Year Cash Flow
1 $1700
2 ?
3 2100
4 2800

Calculating Present Values:
You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $500,000 per year. Thus, in one year, you received $1.5 million. In two years you get $2 million, and so on. If the appropriate interest rate is 9 percent, what is the present value of your winnings?

Present Value and Multiple Cash Flows:
What is the present value of $4000 per year, at a discount rate of 10 percent, if the first payment is received 8 years from now and the last payment is received 25 years from now?

Solution Preview

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Calculating Interest rates:
In January 2007, the average house price in the US was $314,600. In January 2000, the average price was $200,300.
What was the annual increase in selling price?
The total seven year percent increase is ($314,600 - $200,300)/$200,300 = 0.570644 = 57.50644%
The annual rate is then (1+0.570644)^(1/7)- 1 = 0.066623 = 6.66%.

Calculating the Number of Periods:
You’re trying to save to buy a new $170,000 Ferrari, You have $40,000 today that can be invested at your bank. The bank pays 5.3 percent annual interest on its accounts. How long will it be before you have enough to buy the car?
$40,000(1+.053)^n = $170,000
(1+.053)^n = $170,000/$40,000
(1+.053)^n = 4.25
ln((1+.053)^n) = ln(4.25)
n*ln((1+.053) = 1.446919
n(0.051643) = 1.446919
n=1.446919 /0.051643
n = 28.01759
Check: $40,000(1+.053)^28.01759 = $170,000...

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