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Interest Rate Parity

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The Spot Exchange Rate (R) between the British Pound and the Japanese Yen is Y=190.00/L
The six month forward rate (F) is Y=199.0476/L
British six month government bonds offer an interest rate of five percent
Spot Rate (R) is Y184.3/L
Forward Rate (F) is Y199.0476
British 6 month government bonds offer an interest rate of 5% (i)
Japanese six month government bonds are offered at 9.99% (i*)

Formula is: 1+i = (1/R) (1+i*) F= (1+i*) (F/R)
Assuming that the global finance markets are perfectly efficent, what interest rate should the Japanese six-month government bonds be offering? To answer this, use the precise formula above.

The answer is 9.99%

______________________________________________________
(THIS IS THE QUESTION)How is this done mathematically? Where does the British inflation come into this?
Now assume the following:

British Inflation over 6 months period is 3.5%, while Japanese inflation is nil. Has the pound sterling depreciated in nominal terms relative to the yen? Has it depreciated in real terms?

Solution Preview

See attached file for the complete solution.
The Spot Exchange Rate (R) between the British Pound and the Japanese Yen is Y=190.00/L
The six month forward rate (F) is Y=199.0476/L
British six month government bonds offer an interest rate of five percent
Spot Rate (R) is Y184.3/L
Foward Rate (F) is Y199.0476
British 6 month government bonds offer an interest rate of 5% (i)
Japanese six month government bonds are offered at 9.99% (i*)

Formula is: 1+i = (1/R) (1+i*) F= (1+i*) (F/R)
Assuming that the global finance markets are perfectly efficient, what interest rate should the Japanese six-month government bonds be offering? To answer this, use the precise formula above.

The answer is 9.99%

______________________________________________________
(THIS IS THE QUESTION)How is this done mathematically? Where does the British inflation come into this?
Now assume the following:

British Inflation over 6 months period is 3.5%, while Japanese inflation is nil. Has the pound sterling depreciated in nominal terms relative to the yen? Has it depreciated in real terms?

Part 1
When the interest rates are stated they are annualized interest rates
Thus if it is stated that the British six month government bonds offer an interest rate of five percent
It means that the interest one gets for holding British bond worth ₤1000 for 6 months is
25 =1000*(5%)*6/12

The basis for the formula given is the theory of interest rate parity .
This theory states that the return on both pound deposit and yen deposit should be the same.

This can be demonstrated with the help of the above example.

Suppose I have 1 pound

Alternative 1
I buy six month British government bond worth 1 ₤
At the end of 6 months I would have Principal + Interest = P ( 1+ i₤ * n/12)
P= 1 ₤
i₤ = 5%
n= 6 months

Principal + Interest = P ( 1+ i₤ * n/12)= 1.025 ₤ =1 *(1+5.%*6/12)
Amount at the end of 6 months= 1.025 ₤

Alternative 2
I enter into a forward contract to sell Yen and purchase pounds at 6 month forward ...

Solution Summary

The solution shows steps to arrive at equilibrium interest rate using interest rate parity condition.

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