Question

Suppose a US investor has $11900 to invest and can choose either a US investment paying 2.25% or a foreign investment paying 12%, where e is currently 32. What future e would leave the investor indifferent between investing at home or abroad?

Answer 1

The investment in US pays 2.25% a year.

Amount invested = $11900

Interest rate = 2.25% or 0.0225

Interest earned in one year = Amount invested * Interest rate = $11900 * 0.0225 = $267.75

Amount after one year = Amount invested + Interest earned in one year

Amount after one year = $11900 +$267.75 = $12,167.75

The amount after one year when funds are invested in US is $12,167.75

Now, amount is invested in foreign country.

Amount = $11900

Exchange rate = 32 per $1

Amount after conversion = $11900 * 32 = 380,800

Interest rate = 12% or 0.12

Interest earned = Amount after conversion * Interest rate = 380,800 * 0.12 = 45,696

Amount after one year = Amount after conversion + Interest rate = 380,800 + 45,696 = 426,496

The amount after one year when funds are invested in foriegn location is 426,496

Calculate exchange rate -

Exchange rate = Amount after one year when funds are invested in foriegn location/amount after one year when funds are invested in US

Exchange rate = 426,496/12,167.75

Exchange rate = 35.05 per $1

Thus,

In future, if e is 35.05 then this would leave the investor indifferent between investing at home or abroad.