Suppose that an investor must decide between two investments of equal risk and liquidity.
Suppose one potential investment is a one year certificate of deposit (CD) issued by a US bank
while a second potential investment is a one year CD issued by a British bank.
Let E_{$/£} = the spot ER
E^{e}_{$/£} = the expected
ER one year from now
i_{$} = the oneyear interest rate on a CD in the US (in decimal form)
i_{£} = the oneyear interest rate on a CD in Britain (in decimal form)
The rate of return on the US CD is simply the interest rate on that deposit. More formally,
RoR_{$} = i_{$}
The rate of return on the British CD is more difficult to determine.
If a US investor, with dollars, wants to invest in the British CD she
must first exchange dollars for pounds on the spot market. Use the £s
to purchase the British CD. After one year she must convert £s back
to dollars at the exchange rate that prevails then. The rate of return
on that investment is the percentage change in dollar value during the
year. To calculate this we can follow the procedure below,
Suppose the investor has P dollars to invest (P for principal).
Step 1  Convert the dollars to £.

This is the number of £s the investor
will have at the beginning of the year. 
Step 2  Purchase the British CD and earn interest in £s
during the year.

This is the number of £s the investor
will have at the end of the year. The first term in parentheses returns
the principal. The second term is the interest payment. 
Step 3  Convert the principal plus interest back into dollars
in one year.

This is the number of $s the investor can
expect to have at the end of the year. 
The rate of return in dollar terms from this British investment can be found by calculating the expected
percentage change in the value of the investor's dollar assets over the year, shown below,
After factoring out the P this reduces to,
