7/30/2019 Real vs Nominal Interest Rate Handout

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Nominal vs Real Interest Rates 1 of 2(An Example using Watermelons)

UCSD Economics 110B

Notation:

=1-year nominal interest rate this year (measured in dollars)

= 1-year real interest rate this year (measured in watermelons)

= this years price of watermelons

= the expected price of watermelons next year

= the number of watermelons desired for consumption this year

The Theory:

Suppose that you want to borrow watermelons to consume this year.

If you were able to borrow watermelons this year, you would have to repaywatermelons next year.

Banks dont lend watermelons they lend money.

That means that you will have to borrow money instead of watermelons (but you will beable to use all the money you borrow to buy watermelons).

To buy watermelons this year, you would need to borrow dollars this year.

If you borrow dollars this year, you will have to repay dollars next year.

How many watermelons would dollars buy next year if the price of watermelons is

expected to be ?

You could buy watermelons next year with that amount money.

In summary, we can express the real cost of borrowing watermelons two ways:

If you borrow watermelons this year, you would repay watermelons nextyear.

If you borrow watermelons this year, you would repay watermelons nextyear.

This implies that

7/30/2019 Real vs Nominal Interest Rate Handout

2/2

Nominal vs Real Interest Rates 2 of 2(An Example using Watermelons)

UCSD Economics 110B

More simply we can write the relationship between the real interest rate and the nominal

interest rate as

A Numerical Example

Suppose you want to borrow enough money to buy 10 watermelons this year ( ), and

the price of a watermelon is $2 ( ).

That means you would have to borrow (10 watermelons)($2/watermelon) = $20 In the notation above, we would write .

Suppose further that the nominal interest rate is 10% ( = 0.1).

Thus, if you borrow $20 this year, you will have to pay back $20(1+0.1) = $22 nextyear

In the notation above, we would write .

What is $22 worth to you in terms of watermelons? That is, how many watermelons would yoube able to buy with $22 next year?

To answer this, you need to estimate the price of watermelons next year. Suppose that you think the price of a watermelon will rise to $2.10 next year

( ).

In that case, you would be able to buy $22/$2.1 = 10.5 watermelons next yearif you kept the $22.

That means, in effect, that when you pay back the $22, you are paying back theequivalent of 10.5 watermelons.

Using this information, what is the real interest rate you will pay (in terms of watermelons)?

(the real interest rate is 5%).