AS Level Economics 9708: Real Interest Rates and Inflation's Effect on Borrowers and Lenders

In the economy of Doverland, a saver holds money in a bank account paying a fixed nominal (money) interest rate of $5\%$ per year. Over the same year, the CPI rises from $100$ to $103$ .

Separately, a borrower takes out a personal loan at the start of the year at a fixed nominal interest rate of $4\%$ per year. At the time the loan rate was agreed, both the bank and the borrower expected inflation of around $3\%$ for the year, but the actual rate of inflation over the year, once measured, turns out to be $7\%$ .

(a) Using the approximation real interest rate $=$ nominal interest rate $-$ inflation rate, calculate the real interest rate earned by the saver, given the CPI figures above. [2]

(b) Calculate the real interest rate paid on the loan, using the actual rate of inflation of $7\%$ rather than the $3\%$ that had originally been expected. [2]

(c) Using your answer to part (b), explain whether the borrower or the lender gains from inflation turning out to be higher than expected. [3]

(d) State and explain one other consequence, apart from its effect on borrowers and lenders, that a period of high inflation is likely to have for an economy. [2]

Part (a): The saver’s real interest rate

First find the rate of inflation from the CPI figures given, using the earlier value as the base:

$\text{Inflation rate} = \frac{103-100}{100}\times100 = 3\%$

Using the approximation given in the question:

$\text{Real interest rate} = \text{nominal interest rate} - \text{inflation rate} = 5\% - 3\% = 2\%$

The saver’s real interest rate is $2\%$ : although the account pays $5\%$ in money terms, the purchasing power of the saver’s balance grows by only about $2\%$ once the $3\%$ rise in prices is accounted for.

Part (b): The real interest rate on the loan

The loan’s fixed nominal rate is $4\%$ , but the question asks for the real interest rate calculated using the actual rate of inflation over the year, $7\%$ , not the $3\%$ that had been expected when the rate was agreed:

$\text{Real interest rate on loan} = 4\% - 7\% = -3\%$

The real interest rate on the loan is $-3\%$ .

Part (c): Who gains, the borrower or the lender?

A negative real interest rate means the amount repaid, once adjusted for the rise in prices, is actually worth less in purchasing power than the amount originally borrowed. Because inflation ( $7\%$ ) turned out higher than the $3\%$ that both parties expected when the $4\%$ fixed rate was agreed, the real burden of the debt has been eroded by more than either side anticipated.

This means the borrower gains: they get to repay their loan using money that buys less than expected. The lender (the bank) loses: the interest and capital it receives back is worth less in real terms than it expected to receive when it agreed to lend at $4\%$ . This illustrates a general consequence of unexpectedly high inflation. It redistributes real wealth from lenders to borrowers whenever interest rates are fixed in nominal terms and inflation exceeds what was anticipated.

Part (d): A further consequence of high inflation

Besides its effect on borrowers and lenders, high inflation imposes menu costs on firms. When the general price level is rising, firms must more frequently update the prices shown on price lists, shelf labels, printed catalogues, restaurant menus and online or point-of-sale systems. Reprinting, relabelling and reprogramming all use up real resources (staff time and materials) that could otherwise have been used productively elsewhere, so this is a genuine economic cost that grows with the rate of inflation. (Other valid answers include shoe-leather costs, reduced international price competitiveness, or greater uncertainty discouraging investment.)

Final answers

(a) Saver’s real interest rate $=$ $2\%$
(b) Real interest rate on the loan $=$ $-3\%$
(c) The borrower gains and the lender loses, because the negative real interest rate means the debt is repaid in money worth less than expected
(d) Menu costs. The resources firms use up updating prices more often when inflation is high (or another valid consequence such as shoe-leather costs, reduced competitiveness, or investment uncertainty)