If annualized nominal interest rates in the US and Switzerland are 12% and 8% respectively and the 90-day forward [one-year forward] rate for the Swiss franc is $1.0218, at what current spot rate for the Swiss frank will interest rate parity hold?

Current spot rate for the Swiss frank will interest rate parity hold is $1.0214

Explanation:

As per given data

Annualized nominal interest rates in the US = 12%

Annualized nominal interest rates in the Switzerland  = 8%

90 days forward rate = $1.0218

As we know

According to interest rate parity theory

Forward rate differential = Interest rate differential

( ( F - S ) / S ) x (360/n) = ( ( 1 + ru ) / ( 1 + rs ) ) - 1

Where

F = Forward Rate = $1.0218

S = Spot rate = ?

n = numbers of days = 90 days

ru = Annualized nominal interest rates in the US = 12%

rs = Annualized nominal interest rates in the Switzerland  = 8%

Placing the values in the formula

( ( $1.0218 - S ) / S ) x (360/90) = ( ( 1 + 12% ) / ( 1 + 8% ) ) - 1

( ( $1.0218 - S ) / S ) x 4 = ( 1.12  / 1.08% ) - 1

( ( $1.0218 - S ) / S ) x 4 = 0.037037

( ( $1.0218 - S ) / S ) = 0.037037 / 4

( $1.0218 - S ) / S = 0.00925925

$1.0218 - S = S0.00925925

$1.0218 = S0.00925925 + S

$1.0218 = S1.00925925

S = $1.0218 / 1.00925925

S = $1.0214

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