# Suppose the spot rates for 1 and 2 years are s1=6.3% and s2=6.9% with annual compounding. Recall that in this course interest rates are always quoted on an annual basis unless otherwise specified.

Subject: Business / Finance

Financial Engineering and Risk Management

1.

Lottery payments

A major lottery advertises that it pays the winner $10 million. However this prize money is paid at the rate of $500,000 each year (with the first payment being immediate) for a total of 20 payments. What is the present value of this prize at 10% interest compounded annually?

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point 2.

Sunk Costs (Exercise 2.6 in Luenberger)

A young couple has made a deposit of the first month’s rent (equal to

$1,000) on a 6-month apartment lease. The deposit is refundable at

the end of six months if they stay until the end of the lease.

The next day they find a different apartment that they like just as well,

but its monthly rent is only $900. And they would again have to put a

deposit of $900 refundable at the end of 6 months.

They plan to be in the

apartment only 6 months. Should they switch to the new apartment? Assume

an (admittedly unrealistic!) interest rate of 12% per month compounded monthly.

Stay

Switch

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point 3.

Relation between spot and discount rates

Suppose the spot rates for 1 and 2 years are s1=6.3% and s2=6.9% with annual compounding. Recall that in this course interest rates are always quoted on an annual basis unless otherwise specified. What is the discount rate d(0,2)?

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point 4.

Relation between spot and forward rates

Suppose the spot rates for 1 and 2 years are s1=6.3% and s2=6.9% with annual compounding. Recall that in this course interest rates are always quoted on an annual basis unless otherwise specified. What is the forward rate, f1,2 assuming annual compounding?

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point 5.

Forward contract on a stock

The current price of a stock is $400 per share and it pays no dividends. Assuming a constant interest rate of 8% per year compounded quarterly, what is the stock’s theoretical forward price for delivery in 9 months?

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point 6.

Bounds using different lending and borrowing rate

Suppose the borrowing rate rB=10% compounded annually. However,

the lending rate (or equivalently, the interest rate on deposits) is

only 8% compounded annually. Compute the difference between the upper

and lower bounds on the price of an perpetuity that pays A=10,000$ per

year.

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point 7.

Value of a Forward contract at an intermediate time

Suppose we hold a forward contract on a stock with expiration 6

months from now. We entered into this contract 6 months ago so that when we entered into the contract, the expiration was T=1 year. The stock price$ 6 months ago was S0=100, the

current stock price is 125 and the current interest rate is r=10%

compounded semi-annually. (This is the same rate that prevailed 6 months ago.) What is the current value of our forward contract?

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