Assume that spot interest rates are as follows:

Compute the price of a bond with coupon rate 5% and 2 years to maturity.

• $100
• $101
• $103
• $105
• $107

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

You are given the following spot rates:

Compute the forward rate between years 1 and 3.

• 3.15%
• 3.25%
• 3.5%
• 3.75%
• 3.95%

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

You are given the following information:

All coupon payments are annual and par values are 100. Compute the annual forward rate from year one to year two

• 4.5%
• 4.75%
• 5%
• 5.25%
• 5.5%

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

The Wall Street Journal gives the following prices for zero coupon bonds (with a principal of 100):

Compute the yield to maturity of a 2-year coupon bond with a principal of 100 and a coupon rate of 4.25%. Assume annual coupon payments.

• 4%
• 4.25%
• 4.5%
• 4.75%
• 5%

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

The term structure of spot interest rates is given in the table below:

You have just signed a lease on an office building with a rental payment of $1 million per year forever. The first payment is due one year from now.

What is the present value of the lease?

• 22M
• 23M
• 24M
• 25M
• 26M

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

Yankee Inc. has sold the Super Coupon Absolute Marvel (SCAM) security to raise new funds. Unlike ordinary bonds, it pays no par value/face value at the end of its life. It only pays coupons every year as follows: $100(1 + 0.05) at the end of year one, $100(1 + 0.05)2 at the end of year two, and so on. This security lasts for 4 years (i.e., makes 4 payments). The current interest rate is 5% for all maturities.

What is the duration today of SCAM?

• 1.5
• 2
• 2.5
• 2.75
• 3.25

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

You manage a pension fund, and your liabilities consist of two payments as follows:

Your assets are $18 million. The term structure is currently flat at 5%.

Compute an approximate change in the present value of your liabilities, using duration, when interest rates fall by 0.25%.

• 0.8M
• 0.85M
• 0.9M
• 0.95M
• 1M

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

Which of the following investments is most affected by changes in the level of interest rates? Suppose interest rates go up or down by 50 basis points (± 0.5%). Rank the investments from most affected (largest change in value) to least affected (smallest change in value).

• $1 million invested in short-term Treasury bills.
• $1 million invested in Treasury strips (zero coupons) maturing in December 2016.
• $1 million invested in a Treasury note maturing in December 2016. The note pays a 5.5% coupon.
• $1 million invested in a Treasury bond maturing in January 2017. The bond pays a 9.25% coupon.

• II > I > IV > III
• I > II > III > IV
• IV > III > II > I
• II > III > IV > I
• II > III > I > IV

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

You are given the following information about the purchase of a home:

• The home was purchased on Jan 1 2010 for $300,000
• The buyer used a 10-year mortgage to purchase the home with a down payment of $100,000
• The nominal interest rate for the mortgage is 4%, payable at the end of every month
• The buyer sold the home at the end of 2014 for $440,000
• If the buyer hadn't purchased the home, he would have rented a three bedroom apartment. The monthly rent for a three bedroom apartment, payable at the beginning of the month, was $1,300 on Jan 1 2010 and $1,800 on Jan 1 2015
• The rent on the apartment was adjusted at the start of each year and grew at a constant annual rate

Using only the information above (ignore all other expenses), approximate the effective annual rate of return for this real estate investment.

• 15.26%
• 18.26%
• 20.26%
• 22.26%
• 24.26%