Caffieneland is a small country in Central America. The main product of the country is coffee, which is currently priced at $$1\mathrm{.}20$ per cup. Inflation is expected to be $3\%$ per year, and the nominal interest rate is $10\%$ per year.

a$.$ Calculate the real interest rate.

b$.$ Suppose you wanted to borrow $1000$ cups of coffee now, and pay back the loan next year. How many cups of coffee would you owe? What is the interest rate for this coffee loan? Hint: Borrow money now and use it to buy coffee at the current price. Then calculate how much you owe in dollars next year. Use next year$$s coffee price to determine how much you owed in terms of $$cups of coffee.$$