In November 2020, the price level in the U.S. was
𝑃
𝑈
𝑆
=
132
. At the same date, the price level in the Eurozone was
𝑃
𝐸
𝑈
=
98
. One year later, the price levels were
𝑃
𝑈
𝑆
=
128
and
𝑃
𝐸
𝑈
=
102
. During this 12-month period, the real exchange rate was constant. The nominal exchange rate (E) is reported in euros per dollar (i.e., how many euros do we need to purchase one dollar). Using the information above, calculate the rate of change of E during this time (in percent).

Round your answer to the nearest tenth of a percent.

Question

In November 2020, the price level in the U.S. was 
𝑃
𝑈
𝑆
=
132
. At the same date, the price level in the Eurozone was 
𝑃
𝐸
𝑈
=
98
. One year later, the price levels were 
𝑃
𝑈
𝑆
=
128
 and 
𝑃
𝐸
𝑈
=
102
. During this 12-month period, the real exchange rate was constant. The nominal exchange rate (E) is reported in euros per dollar (i.e., how many euros do we need to purchase one dollar). Using the information above, calculate the rate of change of E during this time (in percent).

Round your answer to the nearest tenth of a percent.

BlackTom AI · Accepted Answer

We start by identifying the key concept: the real exchange rate (RER) is the relative price of foreign goods in terms of the domestic currency, adjusted for price level differences. When E is the nominal exchange rate quoted as euros per dollar, a common definition is RER = (E * P_US) / P_EU, where P_US is the domestic (U.S.) price level and P_EU is the foreign (Eurozone) price level.

Given data for time 0 (initial): P_US0 = 132, P_EU0 = 98, and E0 is unknown. For time 1 (after 12 months): P_US1 = 128, P_EU1 = 102, and E1 is unknown. We are told the real exchange rate is constant over the period, so RER0 = RER1.

Set up the equality using the RER formula:
(E0 * P_US0) / P_EU0 = (E1 * P_US1) / P_EU1
Plug in the numbers:\(E0 * 132) / 98 = (E1 * 128) / 102
Rearrange to relate E1 to E0:
E1 / E0 = (132/98) / (128/102) = (132 * 102) / (98 * 128)
Compute the fractions: 132/98 ≈ 1.34694 and 128/102 ≈ 1.25490. Their ratio is ≈ 1.34694 / 1.25490 ≈ 1.0734.
Thus E1 ≈ E0 * 1.0734, meaning the nominal exchange rate (euros per dollar) rose by about 7.34% over the year.

To express the rate of change in percent, we take (E1 − E0) / E0 × 100% ≈ 7.34%.

Rounding to the nearest tenth of a percent gives approximately 7.4%.

Note: If someone uses a different definition of real exchange rate or a different normalization, the numerical result could differ. For example, misapplying a formula or misinterpreting E (e.g., using dollars per euro instead of euros per dollar) could yield a different percent change. With the standard real exchange rate definition used here, the calculated rate of change is about 7.4%.

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