Question

For $9,800 you purchase a T-bill that will pay $10,000 in 76 days. What is your yield to maturity? If the rate of inflation is 5%, what is your real rate of return? Be sure to both to show how you caculuated your answer and to define all the variables in any mathematical equation you use. If prevailing nominal interests hover around 8%, would this be a lucrative purchase?

Answer 1

76 days = (76/365) years = 0.21 years

(i) Yield to maturity being R% (per year),

$9,800 x (1 + R)^0.21 = $10,000

(1 + R)^0.21 = $10,000 / $9,800 = 1.0204

Taking (1/0.21)^th root on both sides,

1 + R = 1.1010

R = 0.1010

R = 10.10%

(ii) Real rate of return = Nominal yield to maturity - Inflation rate = 10.10% - 5% = 5.10%

(iii) If prevailing nominal interest rate is 8%, this is a lucrative purchase because nominal yield to maturity is higher than the prevailing interest rate (10.10% > 8%).