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One day I purchase €$N_1$ at an exchange rate of £1 = €$R_1$, for a cost of £$\frac{N_1}{R_1}$

The next day I purchase €$N_2$ at an exchange rate of £1 = €$R_2$, for a cost of £$\frac{N_2}{R_2}$

How do I calculate the "average" exchange rate, i.e. what is the equivalent exchange rate $R$ such that if I purchased €$(N_1+N_2)$ I would have spent the same amount?

How can I generalise that to more than two transactions?

jonnybolton16
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1 Answers1

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I've since figured out the solution to this.

The total amount of £ spent is $\sum_i\frac{N_i}{R_i}$, which can equivalently by written as $\frac{N}{R}$, where $N=\sum_iN_i$ is the total amount of € bought.

Rearranging for $R$ gives $R=\left(\sum_iN_i\right) / (\sum_i\frac{N_i}{R_i})$

jonnybolton16
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    and this is a weighted harmonic average where weights are $N_i$ and the variables being averaged are $R_i$ – baibo Mar 30 '24 at 11:11