The following information is about current spot rates for Second Duration Savings' assets (loans) and liabilities (CDs). All interest rates are fixed and paid annually $$\begin{array} { | c | c | }
\hline \text { Assets } & \text { Liabilities } \
\hline \text { 1-year loan rate: } 7.50 \text { percent } & \text { 1-year CD rate: } 6.50 \text { percent } \
\hline \text { 2-year loan rate: } 8.15 \text { percent } & \text { 2-year CD rate: } 6.65 \text { percent } \
\hline
\end{array}$$
-What is the duration of the two-year loan (per $100 face value) if it is selling at par?
A)2.00 years
B)1.92 years
C)1.96 years
D)1.00 year
E)0.91 years

Question

The following information is about current spot rates for Second Duration Savings' assets (loans) and liabilities (CDs). All interest rates are fixed and paid annually $$\begin{array} { | c | c | } 
\hline \text { Assets } & \text { Liabilities } \
\hline \text { 1-year loan rate: } 7.50 \text { percent } & \text { 1-year CD rate: } 6.50 \text { percent } \
\hline \text { 2-year loan rate: } 8.15 \text { percent } & \text { 2-year CD rate: } 6.65 \text { percent } \
\hline
\end{array}$$
-What is the duration of the two-year loan (per $100 face value) if it is selling at par?
A)2.00 years
B)1.92 years
C)1.96 years
D)1.00 year
E)0.91 years

Quizplus · Accepted Answer

To find the duration of a bond, we need to calculate the weighted average of the time to receive the bond's cash flows, with each cash flow weighted by the proportion of the bond's present value that it represents. 
For the two-year loan selling at par, we can assume a face value of $100 and two annual cash flows of $7.50 (year 1) and $107.50 (year 2), which gives us a total present value of $100. The weights of the cash flows are 1/100 for the first year and 107.50/100 for the second year.
Thus, the duration of the loan is (1/100)×1 + (107.50/100)×2 = 1.92 years.
Therefore, the answer is B.
The best choice is to hold the two-year loan as it has a higher interest rate than the CDs, and its duration is comparable to that of the 2-year CD.

The Following Information Is About Current Spot Rates for Second