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Valuing a Currency Repayment for a Short-Term Loan

Article Quant Q&A · Author: Graviton
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Summary

The document asks how much euros would fairly repay a friend who advanced 100 US dollars for a purchase, given exchange quotes with different buy and sell rates. The answers frame the payment as a loan valuation problem: convert the dollars at the rate relevant when the money was lent, then account for the time value of money over the lending period. One answer suggests compounding a euro short-term interest rate; another describes the principle as a no-arbitrage repayment equal to the original value plus applicable interest.

The responses do not calculate a specific euro amount from the quoted exchange rates. They also leave practical details unresolved, including the exact lending and repayment dates, which side of the exchange spread applies, and the interest convention. The exchange quotes alone therefore do not determine a unique fair repayment without specifying those assumptions.

Key ideas

  • A currency repayment can be framed as repaying the loan’s value at origination plus interest.
  • The relevant conversion rate depends on the direction of the exchange and the quoted bid-ask spread.
  • A no-arbitrage framing incorporates the time value of the borrowed funds.
  • The document does not specify enough timing and rate conventions to calculate one definitive repayment.

Tags

ForexStatistics
Full text
# The Fair Value of Paying in Currency X for Goods Bought in Currency Y


# The Fair Value of Paying in Currency X for Goods Bought in Currency Y












Me and my friends are from Europe, we went to US. At the end of the trip they bought an item worth $USD 100$, but because they were short of money, so I paid for the item first with my own $USD 100$.

After we came back from Europe, they would have to pay me. They would like to pay me in EUR. What is the fair amount of EUR they should pay me?

Assuming that at money exchange counter, the rates are as follow ( buy/sell are from their perspective):

1 USD buys 1 EUR

1 EUR buys $\frac{1}{1.05}$ USD.

## Answer by TheBridge (score 1)

https://quant.stackexchange.com/a/922

Not realy a quant question but funny though,

Here are my two euro-cents,

I would say that you should ask them for 100-USD times the exchange rate at the date you lend them, plus the interest rates amount that can be calculated by compounding EUR EONIA rate on the period you lend them that money.

Regards

## Answer by finitud (score 0)

https://quant.stackexchange.com/a/968

This is just a no-arbitrage argument: whatever you paid for the 100 USD plus the corresponding interest rate.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.