# Calculating discount rate

#### Tom Sun

This is totally a newbie question, but I'm going through the Columbia FE course on coursera. I'm a little stuck on this one quiz question, can someone lend me a hand on this?

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)?

Thanks.

#### Varun Dubey

is 7.5% an option?

#### Tom Sun

7.5% was the forward rate, but maybe the discount rate is 1/1.075?

#### Varun Dubey

d(0,2) = 1/(1+0.069)^2 = 0.875

• smriti and Tom Sun

#### smriti

I'm a little stuck on this one quiz question, can someone lend me a hand on this?
1 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?

2
Suppose the borrowing rate r_B = 10\%rB =10% compounded annually. However,
the lending rate (or equivalently, the interest rate on deposits) is
only 8\%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.

3
Suppose we hold a forward contract on a stock with expiration 66
months from now. We entered into this contract 66 months ago so that when we entered into the contract, the expiration was T = 1T=1 year. The stock price\$ 66 months ago was S_0 = 100S0=100, the
current stock price is 125125 and the current interest rate is r = 10\%r=10%
compounded semi-annually. (This is the same rate that prevailed 66 months ago.) What is the current value of our forward contract?

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