Question

Boris Borrower and Lynn Lender agree that Lynn will lend Boris $\mathrm{\$}10,000$ and that Boris will repay the $\mathrm{\$}10,000$ with interest in one year. They agree to a nominal interest rate of $8\mathrm{\%}$, reflecting a real interest rate of $3\mathrm{\%}$ on the loan and a commonly shared expected inflation rate of $5\mathrm{\%}$ over the next year. a. If the inflation rate is actually $4\mathrm{\%}$ over the next year, how does that lower-than-expected inflation rate affect Boris and Lynn? Who is better off? b. If the actual inflation rate is $7\mathrm{\%}$ over the next year, how does that affect Boris and Lynn? Who is better off?

Short answer

With a 4% inflation rate, Lynn is better off, as she effectively receives a higher real interest rate than expected (4% vs 3%). With a 7% inflation rate, Boris is better off, as the real interest rate he pays is lower than expected (1% vs 3%).

Step-by-step solution

Understanding the Effect of Inflation on Real Interest Rate

Real interest rate can be calculated with the formula: Real interest rate = Nominal interest rate - Inflation rate. If the inflation is lower than expected, the real interest rate is higher than initially agreed upon.

Calculate Real Interest Rate with a 4% Inflation

Substitute the 4% actual inflation rate into the formula: Real Interest Rate = 8% - 4%. This shows that the real interest rate Boris will end up paying is 4%.

Determine Who Is Better Off with Lower Inflation

Lynn is better off with a 4% inflation rate because the real interest rate she receives is higher than the initially expected 3%. This means Lynn gets more real value back. Conversely, Boris is worse off as he is paying a higher real interest rate than expected.

Calculate Real Interest Rate with a 7% Inflation

Substitute the 7% actual inflation rate into the formula: Real Interest Rate = 8% - 7%. This gives us a real interest rate of 1%.

Determine Who Is Better Off with Higher Inflation

Boris is better off with a 7% inflation rate because the real interest rate he is paying is lower than expected, only 1%. Lynn, on the other hand, receives less real value from the interest due to the higher inflation, making her worse off.

Key concepts

Inflation Rate

The inflation rate is a critical economic indicator reflecting the overall rise in price level of goods and services in an economy over a period of time. Understanding the inflation rate is essential when dealing with loans and savings. For instance, in Boris and Lynn's agreement, a predicted inflation rate of 5% was factored into the nominal interest rate to arrive at the expected real interest rate.

However, if the actual inflation rate turns out to be 4%, this lower-than-expected inflation implies that the purchasing power of the money Lynn lends does not decrease as quickly as anticipated. Therefore, Lynn benefits as the real value of the money repaid (including interest) is higher. On the other hand, Boris, who is repaying the loan, will find that he has to deliver more in terms of purchasing power than he had prepared for, effectively making the loan more expensive for him.

Nominal Interest Rate

The nominal interest rate is the percentage increase in money that the borrower agrees to pay the lender, without any adjustment for inflation. In the given scenario, Boris and Lynn agreed on an 8% nominal interest rate for the loan. This rate does not change regardless of what happens with inflation.

It's important to understand that the nominal interest rate is what is commonly quoted when you take out a loan or save money in bank accounts. However, it does not provide a complete picture of the cost or benefit of the loan as it does not consider the purchasing power of the money at the time of repayment. This is why the real interest rate, which does account for inflation, is often a more accurate measure of the cost of borrowing or the yield on savings.

Loan Repayment

Loan repayment refers to the act of paying back money previously borrowed from a lender. The repayment includes not only the original amount borrowed (the principal) but also interest. The real interest rate plays a vital role in understanding the true cost of the loan. With Boris's loan of $10,000, he agrees to repay it with interest after one year.

The actual amount Boris will repay can vary with the inflation rate. The agreed nominal rate is the baseline, but as shown with the varying inflation rates (4% and 7%), the real burden of repayment can either increase or decrease. Thus, when taking a loan, it is pivotal to consider potential variances in inflation as this may affect the real amount of money that will be repaid in the future.

Economic Effects of Inflation

Inflation has significant economic effects, influencing the decision-making of lenders and borrowers, like Lynn and Boris. When inflation is high, lenders like Lynn receive less real value at the end of the loan term because the money returned has less purchasing power than the money originally lent. Conversely, borrowers like Boris benefit from high inflation as they end up paying back less in real terms.

However, if inflation is lower than expected, the opposite is true. Lenders benefit from lower inflation as they get back money with greater purchasing power than what was expected. Borrowers pay more in real terms than they expected. Therefore, inflation not only affects the value of money over time but also impacts key economic decisions regarding saving, investing, and spending.