Question

Problem 17-02
Interest Rate Parity

The nominal yield on 6-month T-bills is 7%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 4%. In the spot exchange market, 1 yen equals $0.011. If interest rate parity holds, what is the 6-month forward exchange rate? Round the answer to five decimal places. Do not round intermediate calculations.

Thanks for the help!

Answer 1

Solution:

As per the Interest rate Parity model

Exchange rate differential = Interest rate differential

( Forward Rate / Spot Rate ) = [ ( 1 + Interest Rate in Currency A ) / ( 1 + Interest Rate in Currency B ) ]

As per the Information given in the question we have

U.S. Interest rate on T – Bills = 7 % = 0.07 ( Annualized )

Thus U.S. Interest rate for 6 Months

= 7 % * ( 6 / 12 ) = 3.5 % = 0.035

Japanese Interest rate on default free bonds = 4 % = 0.04   ( Annualized )

Thus Japanese Interest rate for 6 Months

= 4 % * ( 6 / 12 ) = 2 % = 0.02

Spot rate of the Yen is = $ 0.011

Thus $ / ¥ = A/ B = $ 0.011

Applying the above values in the formula / Equation we have the six month forward exchange rate as follows :

Forward Rate / $ 0.011= [ ( 1 + 0.035 ) / ( 1 + 0.02 ) ]

Forward Rate = [ 1.035 / 1.02 ] * $ 0.011

Forward Rate = 1.014706 * $ 0.011

Forward Rate = $ 0.011162

Forward Rate = $ 0.01116 ( when rounded off to five decimal places )

Thus the 6 month forward exchange rate for the Yen = $ 0.01116