Question

You have a treasury bond that pays
$
100
$100 one year from today and
$
1
,
100
$1,100 two years from today.

You notice that the yield-to-maturity on a one year-zero coupon treasury bond is
1
%
1% and the yield-to-maturity on a two year-zero coupon treasury bond is
2
%
2%. What should the price of your bond be?


1
,
177.44
1,177.44



1
,
156.30
1,156.30



1
,
223.46
1,223.46



1
,
246.37
1,246.37


1 point
Coursera Honor Code

Answer 1

To calculate the price of your treasury bond, we need to discount the cash flows of the bond using the corresponding yields.

The bond pays:
- $100 one year from now
- $1,100 two years from now

Given the yields:
- The yield on a one-year bond is 1%, which means we will discount the $100 cash flow using this yield.
- The yield on a two-year bond is 2%, which means we will discount the $1,100 cash flow using this yield.

### Step 1: Calculate the present value of the cash flows

1. **Present value of $100 one year from now:**

\[
PV_1 = \frac{100}{(1 + r_1)} = \frac{100}{(1 + 0.01)} = \frac{100}{1.01} \approx 99.01
\]

2. **Present value of $1,100 two years from now:**

\[
PV_2 = \frac{1100}{(1 + r_2)^2} = \frac{1100}{(1 + 0.02)^2} = \frac{1100}{(1.02)^2} = \frac{1100}{1.0404} \approx 1057.73
\]

### Step 2: Add the present values to get the total price of the bond

\[
\text{Price of the bond} = PV_1 + PV_2 \approx 99.01 + 1057.73 \approx 1156.74
\]

Given the options, the closest price of your bond would be:

\[
\approx 1,156.30
\]

So, the correct answer is:

**$1,156.30**