Judy Johnson is choosing between investing in two Treasury securities
that mature in five years and have par values of $1,000. One is
a Treasury note paying an annual coupon of 5.06 percent. The other
is a TIPS which pays 3 percent interest annually.
a. If inflation remains constant at 2 percent annually over the
next five years, what will be Judy’s annual interest income
from the TIPS bond? From the Treasury note?
b. How much interest will Judy receive over the five years from
the Treasury note? From the TIPS?
c. When each bond matures, what par value will Judy receive
from the Treasury note? The TIPS?
d. After five years, what is Judy’s total income (interest � par)
from each bond? Should she use this total as a way of deciding
which bond to purchase
Judy Johnson is choosing between investing in two Treasury securities that mature in five years and have par values of $1,000. One is a Treasury note paying an annual coupon of 4.35 percent. The other is a TIPS that pays 3.75 percent interest annually.
a) If inflation remains constant at 2.8 percent annually over the next five years, what will be Judy’s annual interest income from the TIPS bond? From the Treasury note?
b) How much interest will Judy receive over the five years from the Treasury note? From the TIPS?
c) When each bond matures, what par value will Judy receive from the Treasury note? From the TIPS?
d) After five years, what is Judy’s total income (interest + par) from each bond? Should she use this total as a way of deciding which bond to purchase?
a. To calculate Judy's annual interest income from the TIPS bond, we need to multiply the par value ($1,000) by the annual interest rate (3%) and then adjust for inflation. Since inflation remains constant at 2% annually, we need to adjust the interest rate by subtracting the inflation rate from the nominal interest rate:
Annual interest income from TIPS bond = Par value * (Nominal interest rate - Inflation rate)
= $1,000 * (3% - 2%)
= $1,000 * 1%
= $10
Similarly, to calculate Judy's annual interest income from the Treasury note, we use the same formula:
Annual interest income from Treasury note = Par value * Coupon rate
= $1,000 * 5.06%
= $1,000 * 0.0506
= $50.60
b. To calculate the total interest Judy will receive over the five years from each bond, we need to multiply the annual interest income by the number of years:
Total interest from Treasury note = Annual interest income from Treasury note * Number of years
= $50.60 * 5
= $253
Total interest from TIPS bond = Annual interest income from TIPS bond * Number of years
= $10 * 5
= $50
c. When each bond matures, Judy will receive the par value of each bond, which is $1,000 for both the Treasury note and TIPS bond.
d. To calculate Judy's total income (interest + par value) from each bond after five years, we need to add the total interest received from each bond to the par value:
Total income from Treasury note = Total interest from Treasury note + Par value
= $253 + $1,000
= $1,253
Total income from TIPS bond = Total interest from TIPS bond + Par value
= $50 + $1,000
= $1,050
Judy should consider the total income as a way of deciding which bond to purchase. In this case, the total income from the Treasury note is higher, so it may be a more favorable choice for Judy.