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While looking at exchange rates for an upcoming vacation, I decided to brush up on some old math but wanted to make sure I was thinking about it correctly.

$B_1$ charges a rate for USD to EUR conversion of $0.85$ but charges a shipping fee ($F$). I want to calculate the effective rate of $B_1 (B_1')$ with a given $F$ for an amount $A$.

$B_1'*(A+F) = B_1*A$

$or

$B_1' = \dfrac{B_1*A}{A+F}$

So for $F = 10$ and $A = 500$

$B_1' = \dfrac{425}{510}$ or $B_1' = 0.833$

Is this the right way to think about it?

Secondly another bank, $B_2$ offers a lower initial rate of $0.83$ but has no fee. How would one construct a formula to determine the value of $A$ for a given $F$ at which $B_1'$ and $B_2$ are even (practically, when to go with one over the other)?

JMP
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mrturtle
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1 Answers1

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Well you have $$ B_2 = B_1' = \frac{B_1 \cdot A}{A+F} $$ which you need to solve for $A$: $$ B_2 (A+F) = B_1 A \\ B_2 F = B_1 A - B_2 A\\ A = \frac{B_2 F}{B_1 - B_2} $$

gt6989b
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