# 1.1. Suppose that you buy a two-year 8% bond at its face value. a) What will be your nominal return over the two years if inflation is 3% in the first year and 5% in the second? What will be your real return? b) Now suppose that the bond is a TIPS. What will be your real and nominal return?

Computation of the True Reprove of Revert
True Reprove of Revert = (Coupon Reprove – Inflation reprove) / (1+Inflation rate)
Where as
Coupon reprove = 0.08
Inflation reprove = 0.03
1st year True revert
True Reprove of Revert = (0.08– 0.03) / (1+0.03)
True Reprove of Revert = 0.049
True Reprove of Revert = 4.9%
Hence the True Reprove of Revert Is 4.9%
(1 + professed reprove) = (1 + true reprove) x (1 + inflation reprove)
(1 + professed reprove) = (1 + 0.049) x (1 + 0.03)
(1 + professed reprove) = (1.049) x (1.03)
(1 + professed reprove) = 1.08047
Professed reprove = 1.08047-1
Professed reprove = 0.08 or 8%
Hence the Professed Reprove is 8%
2st year True revert
True Reprove of Revert = (0.08– 0.05) / (1+0.05)
True Reprove of Revert = 0.049
True Reprove of Revert = 2.9%
Hence the True Reprove of Revert Is 2.9%
(1 + professed reprove) = (1 + true reprove) x (1 + inflation reprove)
(1 + professed reprove) = (1 + 0.029) x (1 + 0.05)
(1 + professed reprove) = (1.029) x (1.05)
(1 + professed reprove) = 1.08045
Professed reprove = 1.08045-1
Professed reprove = 0.081 or 8.1%
Hence the Professed Reprove is 8.1%
b) Now guess that the manacle is a TIPS. What get be your true and professed revert?
Solution:
TIPS media Treasury Inflation-Protected Securities (TIPS)
1st year
True reprove = Coupon reprove – Inflation
True reprove = 0.08-0.03 = 0.05
(1 + professed reprove) = (1 + true reprove) x (1 + inflation reprove)
(1 + professed reprove) = (1 + 0.05) x (1 + 0.03)
(1 + professed reprove) = (1.05) x (1.03)
(1 + professed reprove) = 1.0815
Professed reprove = 1.0815-1
Professed reprove = 0.0815 or 8.15%
Hence the Professed Reprove is 8.15%
2nd years
True reprove = Coupon reprove – Inflation
True reprove = 0.08-0.05 = 0.03
(1 + professed reprove) = (1 + true reprove) x (1 + inflation reprove)
(1 + professed reprove) = (1 + 0.03) x (1 + 0.05)
(1 + professed reprove) = (1.03) x (1.05)
(1 + professed reprove) = 1.0815
Professed reprove = 1.0815-1
Professed reprove = 0.0815 or 8.15%
Hence the Professed Reprove is 8.15%