What will my savings be worth in dollars?

What a local deposit rate leaves once the currency it is paid in has fallen against the dollar, year by year. It compares one currency against the dollar, and assumes both the rate and the fall repeat every year, and it is before tax and before any fee on the account, and a certificate that cannot be broken early is not modelled at all.

• The currency is losing faster than the rate pays. The balance grows in figures every year and is worth less in dollars every year.

After 5 years your statement says 248,832, and at today's exchange rate that is worth 81,537 in dollars. The difference of 167,295 is what the fall in the currency took, assuming nothing is added or withdrawn.

The balance grows at the rate the deposit pays and shrinks by whatever the currency loses against the dollar. Those are two separate compounding effects and they do not cancel by subtraction: what is left is the balance multiplied by one plus the rate, divided by one plus the fall, both raised to the number of years.

The figure is printed in the units you started in, and that is a deliberate choice rather than a shortcut. It is the dollar value of the balance, converted back at today's exchange rate — so a reader who put in 100,000 can read the answer against the 100,000 they typed without a second currency appearing anywhere on the page. The sub-line says so under the figure, because a bare number here would otherwise read as the local balance and the whole point would invert.

A rate of 20% against a fall of 25% is the case worth sitting with. The statement grows every year and the answer falls every year, and both are true at once. A saver in Cairo holding a certificate through that period was not making a mistake about arithmetic; they were reading one of two numbers, and only one of them was printed on the certificate.

Where the currency gains rather than falls, the same division runs the other way: the bars rise above the statement line and the row names a gain. Nothing about the method changes.

balance × (1 + rate)^years ÷ (1 + fall)^years

The rate compounds the balance up; the fall in the currency divides it back down. The result is the dollar value, written in the units you started in.

A worked example

Put 100,000 on a deposit paying 20% a year while the currency loses 25% a year. After five years the statement says 248,832 and the dollar value is 81,537 — a balance that has grown by a factor of two and a half and is worth a fifth less than what you started with.

What it assumes

• The rate is fixed for the whole period and compounds once a year. Deposit rates in a falling currency reprice more often than that, usually after the fall rather than before it.
• The currency falls by the same amount every year. Real currencies do not — they hold and then move in a single step — and a fall arriving in one year does more damage to a balance than the same fall spread over five.
• Nothing is added to or taken out of the balance, and the deposit runs the full term. Breaking a certificate early usually costs the accrued return, which this does not model.
• Tax and account fees are not modelled. Where either applies it comes off the rate before this calculation starts, so enter the rate you actually receive rather than the advertised one.