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In: Finance

An inflation-indexed Treasury bond has a par value of $5,000 and a coupon rate of 7...

An inflation-indexed Treasury bond has a par value of $5,000 and a coupon rate of 7 percent. An investor purchases this bond and holds it for one year. During the year, the consumer price index decreases by 1.5 percent first six months of the year, and by 2.25 percent during the second six months of the year due to a deflation. What are the total interest payments the investor will receive during the year?

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Solutions

Expert Solution

Treasury Inflation-Protected Securities are securities that  provide safeguard against inflation. The principal of a TIPS increases with inflation and decreases with deflation, as measured by the Consumer Price Index (CPI)

We can calculate the interest as below.

For first 6 months CPI decrease by 1.5% ie we have to adjust the principal with this .

New Principal = 5000 * ( 1 - .015 / 2)

=5000 * (1 - 0.0075)

= 4962.50

Interest for the first 6 months = Principal * coupon * 6 / 12

= 4962.50 * 7 /100 * 0.5

= 173.69

For next 6 months CPI decrease by 2.25% ie we have to adjust the principal with this

New Principal = 4962.50 * ( 1 - 0.0225/2)

= 4962.50 * ( 1 - 0. 01125)

= 4906.67

Interest for the next six months = 4906.67 * 7% * 0.5

= 171.73

Total interest payments = 173.69 + 171.73

= $345.42

Time Deflation Prinicipal Coupon Interest Payment
Annual Semiannual Annual Semiannual
0.0 5000.00
0.5 1.50% 0.75% 4962.50 7% 3.50% 173.69
1.0 2.25% 1.125% 4906.67 7% 3.50% 171.73
Total 345.42

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