This question can be answered without the need to work through the duration calculation.
Remember that duration is related to maturity and to the coupons of a bond. A zero coupon bond has a duration the same as its remaining maturity. A coupon paying bond has a duration less than its maturity.
In this case there are three semi-annual periods left (i.e., 1.5 years). As the bond is a coupon bond its duration must be less than 1.5.
Remember that duration measures how long it takes on average to receive the cash flows from a bond. In this case the cash flows are:
6 months: $30
12 months: $30
18 months: $1,030
Notice we have to wait three periods for the majority of our cash flows. This means that the duration is likely to be just a bit lower than 1.5.
Remember we can calculate duration if needed as well as follows:
Time |
CF |
DF |
PV |
PV × t |
1 |
30 |
1/1.02 |
29.41 |
29.41 |
2 |
30 |
1/1.022 |
28.83 |
57.66 |
3 |
1,030 |
1/1.023 |
970.59 |
2,911.77 |
|
|
|
1,028.83 |
2,998.84 |
2998.84 / 1,028.83 = 2.915 half years, so (2.915 / 2) = 1.457 years