# Working out interest rates on a futures contract/exchange rates contract.

okay my main problem is I have to work out a $3$ month interest rate for the us dollar. The question I'm stuck on is At the end of trading on $1$ January $2012$ the dollar/pound spot exchange rate was $\$ 1.5700$per pound and the three month forward rate was$\$1.5825$ per pound. answer the following:

estimate the us interest rate for the next quarter if the interest rate on risk free pound deposits in the uk for the next quarter is $0.125\%$ ($90$ day rate).

my solution given by the lecturer just says

$F = S \frac{1+r}{1+r£}$ where $F$ is the forward rate, $S$ is the spot exchange rate and $r$ stands for the interest rate $$1.5825 = 1.5700 (1+r)/1.00125$$ (re arranging from this line is where i become confused ) $r= 0.9222\%$

any help would be appreciated, cheers :)

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You want to solve the equation $$1.5825=\frac{1.5700(1+r)}{1.00125}.$$ We want to "isolate" $r$. First multiply both sides by $1.00125$. We get $$(1.5825)(1.00125)=1.5700(1+r).$$ Better, the $r$ is less buried. Now divide both sides by $1.5700$. We get $$\frac{(1.5825)(1.00125)}{1.5700}=1+r.$$ Now it is time to use the calculator. Mine gives that the left side is equal to $1.0092217$. Of course this is not exact, but it is pretty close. Your instructor seems to have rounded this up very slightly.

Subtract $1$ to get $r$. We get $r=0.0092217$. Now as usual to express this in percent, multiply by $100$. We get $0.92217\%$.

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thank you so much that makes way more sense than my lecturer. his notes for this exam are terrible..! sorry about the poor posting it was my first time, thanks again! – Drew Goodwin Aug 9 '12 at 3:34