Compound interest in two currencies: the same rate is a gain in one and a loss in the other

What does it mean?

Compound interestTermCompound interest×الفائدة المركبةReturns calculated on your original money and on every return before it, so the balance grows on itself year after year.Open the term is a return that earns a return, and the arithmetic describing it is the same everywhere. Leave a balance in an account paying a rate, and the second year’s rate applies to the first year’s ending figure rather than to what was originally deposited. A bank in Cairo and a bank in Riyadh apply that identically. A calculator does not ask where you are before it answers.

What the calculation produces is a count of currency units. That is the part that is not the same in both places, because the two countries do not run the same kind of unit. The riyal is pinned to the dollar at a level the central bankTermCentral bank×البنك المركزيThe government's bank, which controls the money supply, sets interest rates, and oversees all other banks in the country.Open the term defends with its reserves. The pound is priced by the market, and the market has repriced it heavily twice inside a decade.

So the same formula answers a different question depending on where it is used. In one place it produces a figure close to what the money will actually buy. In the other it produces a figure that will appear on a statement and leaves the more useful question open.

This is the calculation NOUQUD’s compound interest guide stops short of. That guide says the calculator reports a nominal balance, and that converting a nominal balance into purchasing power is a separate piece of arithmetic. This is that arithmetic, run twice.

Why should I care?

Because the gap between the two answers is not a rounding error, and it does not run in the direction the interest rateTermInterest rate×سعر الفائدةThe percentage of principal charged by a lender or paid by a saver, usually stated as an annual rate.Open the term suggests.

Hold the rate identical and the outcomes still diverge completely. Take 100,000, leave it for five years at 10% a year, and the balance is 161,051 in either country. Same inputs, same formula, same answer. Now price it. Saudi consumer prices rose about 12% between 2021 and 2025. Egyptian prices rose about 126% over the same five years. The Saudi saver’s 161,051 buys roughly what 143,600 bought at the start, a real gain of about 44%. The Egyptian saver’s 161,051 buys roughly what 71,100 bought at the start, a real loss of about 29%.

One saver ends up 44% better off and the other 29% worse off, from the same rate over the same term, and nothing anywhere in the compounding formula registers that the two are different.

The rates on offer are not actually the same, and the reason they differ is the reason the outcomes differ. Egypt’s central bank sets its own interest rate, because a floating currency is what buys that freedom, and it has set high ones: the average deposit rate in Egypt in 2024 was 19.2%. Saudi Arabia’s repo rate in December 2024 was 5%, because a peggedTermCurrency peg×ربط العملةA fixed exchange rate between a local currency and another, usually the dollar, so the rate does not move with market supply and demand.Open the term currency imports the interest rate of the currency it is pegged to. The larger number is available in Egypt precisely because the saver there is carrying a currency risk that the peg absorbs on the Saudi saver’s behalf.

Price each against the inflationTermInflation×التضخّمA general rise in prices over time, so one riyal today buys less than it did a year ago.Open the term of the year it was paid. Egyptian inflation in 2024 was 33.3%, which turns 19.2% into a real return of negative 10.6%. Saudi inflation that year was 1.5%, which leaves the 5% repo worth about 3.4% in real terms, and a deposit pays less than the policyTermCar insurance×تأمين السياراتA contract that covers the cost of damage to your vehicle or injury to others, depending on the type of policy you hold.Open the term rate, so that figure is a ceiling rather than what a saver received. The headline rate almost four times larger produced an outcome about fourteen percentage points worse.

A negative real return compounds too, and that is the part most easily missed. Compounding is usually discussed as a force that works in your favor, so the case where it does not tends to be described as simple erosion. It is not simple. Purchasing power falling 10% a year is down about 41% after five years rather than 50%, because each year’s loss applies to what is left rather than to the original sum. It is the same calculation as a compounding gain, running below zero.

That has a direct consequence for what the compound interest guide concluded. Its central finding, that what an account earns passes what you put into it in the tenth year, is a finding about nominal balances. At a negative real rate there is no equivalent crossover, because the growth term never turns positive at all. The moment the guide describes does not arrive late under a high inflation currency. It does not arrive.

What should I know?

Compare real rates and never headline ones. Two deposit products quoted in two currencies are not the same product at two prices, and the number printed on each is not comparable to the other as printed. The figure that survives the move between currencies is the real return, which is the rate adjusted for what prices did over the same period.

Neither saver chose their rate, and neither can. Under a peg, the decision that moves a deposit rate is taken by the central bank of the currency being pegged to, for reasons that have nothing to do with the local economy. Under a float it is taken locally, usually in response to the same conditions that made the saver need a return in the first place. In both cases the rate is weather. The contribution is the part that answers to the saver, which is the same conclusion the compound interest guide reached for a different reason.

A rate quoted for a year in a currency that repriced mid year is not the rate you received. An annual figure assumes the unit it is denominated in held still for the year. Where it did not, the rate describes an average of two different currencies, and the balance at the end is worth less than the arithmetic suggests.

The horizon that is safe to plan against is shorter under a floating currency. A thirty year projection at today’s rate rests on an assumption about the rate wherever it is run. Where that assumption has been wrong by twenty percentage points inside a single year, the projection is a piece of arithmetic rather than a plan, and the longer the term the more of the answer is resting on the part that moved.

None of this is an argument that one arrangement is better run than the other. A peg buys price stability and pays for it with the interest rate. A float buys control of the interest rate and pays for it with the stability of the unit the rate is paid in. Both halves of that trade come out of the same account, and what a currency peg costs sets out the trade itself.