Macroeconomics (Fourth Edition)
Macroeconomics (Fourth Edition)
4th Edition
ISBN: 9780393603767
Author: Charles I. Jones
Publisher: W. W. Norton & Company
Question
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Chapter 7, Problem 5E

(a)

To determine

Calculate the present discounted value of $50,000, which is received 1 year from now.

(a)

Expert Solution
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Explanation of Solution

Present discounted value (x) of $50,000, which is received 1 year from now with 3% interest rate (R), is calculated as follows.

Present discounted value=Future value(1+Rate of interest)Time period        (1)

Substitute the respective values in Equation (1).

x=$50,000(1+0.03)1x=$50,000(1.03)1x=48,544

The present discounted value is $48,544.

(b)

To determine

Calculate the present discounted value of $50,000 received 10 year from now.

(b)

Expert Solution
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Explanation of Solution

Substitute the respective values in Equation (1) to calculate the present discounted value (x) of $50,000 received 10 years from now.

x=$50,000(1+0.03)10x=$50,000(1.03)10x=50,0001.3439x=37,205

The present discounted value is $37,205.

(c)

To determine

Calculate the present discounted value of $100 every year, forever, starting immediately.

(c)

Expert Solution
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Explanation of Solution

The present discounted value of $100 every year, forever, is calculated as follows:

x=100+100(1+R)1+100(1+R)2+100(1+R)3+...=100×[1+100(1+R)1+100(1+R)2+100(1+R)3+...]=100×1111+R=100×1+RR=100×1.030.03=$3,433

The present discounted value is $3,433.

(d)

To determine

Calculate the present discounted value of $100 every year, forever, starting 1 year from now.

(d)

Expert Solution
Check Mark

Explanation of Solution

The present discounted value of $100 every year, forever, starting 1 year from now is calculated as follows:

x=11+R×100×1+RR=11+0.03×100×1.030.03=11.03×100×1.030.03=0.9708×100×34.3333=3,333

The present discounted value is $3,333.

(e)

To determine

Calculate the present discounted value of $100 every year for the next 50 year, starting immediately.

(e)

Expert Solution
Check Mark

Explanation of Solution

The present discounted value of $100 every year, forever, is calculated as follows:

x=100×1(11+R)501(11+R)=100×1(11+0.03)501(11+0.03)=100×1(11.03)5011(1.03)=100×10.228110.9708=100×0.77190.0292=100×26.43=2,643

The present discounted value is $2,643.

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Students have asked these similar questions
Consider a call option on a stock that does not pay dividends. The stock price is $100 per share, and the risk-free interest rate is 10%. The call strike is $100 (at the money). The stock moves randomly with u=2 and d=0.5. 1. Write the system of equations to replicate the option using A shares and B bonds. 2. Solve the system of equations and determine the number of shares and the number of bonds needed to replicate the option. Show your answer with 4 decimal places (x.xxxx); do not round intermediate calculations. This is easy to do in Excel. A = B = 3. Use A shares and B bonds from the prior question to calculate the premium on the option. Again, do not round intermediate calculations and show your answer with 4 decimal places. Call premium =
Answer these questions using replication or the risk neutral probability. Both methods will produce the same answer. Show your work to receive credit. 6. What is the premium of a call with a higher strike. Show your work to receive credit; do not round intermediate calculations. S0 = $100, u=2, d=0.5, r=10%, strike=$150
Answer these questions using replication or the risk neutral probability. Both methods will produce the same answer.
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