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

Maturity (years)	1	2	3	4	5	6
Interest rate (%)	3.5	3.0	4.0	4.0	4.0	4.0

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.

Solution: D

[[math]] \begin{aligned} & P V_1=\frac{1}{1+3.5 \%}=0.9662, P V_2=\frac{1}{(1+3 \%)^2}=0.9426 \\ & \text { From } P V_3 \text { on, sum PV }=1 /(1+4 \%)^3+1 /(1+4 \%)^4+\ldots \\ & =\frac{1}{(1+4 \%)^2}\left(\frac{1}{1.04}+\frac{1}{1.042}+\frac{1}{1.043} \ldots\right) \\ & =\frac{1}{(1+4 \%)^2} \times \frac{1}{0.04}=23.1139 \end{aligned} [[/math]]

Therefore the total = 25.02268

References

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