Question

The Treasury just sold a bunch of 5-year, zero coupon $100 face-value bonds for an interest rate (r_rf) of 6.0%. If r_inf is 2.0% at the time of the sale, then jumps to 3.0% the next day, what is (approximately) r_rf of the bonds on the next day? Assume nothing changes overnight except for the jump in the inflation rate. Hint: Assume r_rf = r_inf + all other treasury bond interest rate risks.

Answer 1

r_rf or nominal interest rate (approximately) = real interest rate + inflation

first we need to calculate real interest rate when bonds were sold.

6% = real interest rate + 2%

real interest rate = 6% - 2% = 4%

r_rf or nominal interest rate (approximately) next day = real interest rate + inflation next day

r_rf or nominal interest rate (approximately) next day = 4% + 3% = 7%

real interest rate doesn't change next day.

(approximately) r_rf of the bonds on the next day is 7%.