Question

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

Short answer

Answer: In the scenario with lower-than-expected inflation (4%), Boris is better off, and Lynn is worse off. In the scenario with higher-than-expected inflation (7%), Boris is worse off, and Lynn is better off.

Step-by-step solution

Understand the given information

Boris borrows \( \$ 10,000\) from Lynn, with a nominal interest rate of \(8 \%.\) The real interest rate agreed upon is \(3 \%\) and the expected inflation rate is \(5 \%.\) Note that the nominal interest rate is the sum of the real interest rate and the expected inflation rate, i.e., \(8\% = 3\% + 5\%\).

Scenario A - Actual inflation rate is \(4\%\)

In this scenario, the actual inflation rate is lower than the expected inflation rate (\(4\%\) instead of \(5\%\)). We need to analyze how this affects Boris and Lynn and determine who is better off. First, calculate the actual nominal interest rate: Actual nominal interest rate = Real interest rate + Actual inflation rate Actual nominal interest rate = \(3\% + 4\% = 7\%\) Now, calculate the total amount Boris has to pay back: Total amount to pay back = Principal + (Principal * Actual nominal interest rate) Total amount to pay back = \(10000 + (10000 * 7\%) = 10000 + 700 = \$ 10,700\) In this scenario, Boris has to pay back a lesser amount compared to the initial agreement based on the expected inflation rate. Therefore, Boris is better off since he gains, and Lynn is worse off as she experiences a loss.

Scenario B - Actual inflation rate is \(7\%\)

In this scenario, the actual inflation rate is higher than the expected inflation rate (\(7\%\) instead of \(5\%\)). We need to analyze how this affects Boris and Lynn and determine who is better off. First, calculate the actual nominal interest rate: Actual nominal interest rate = Real interest rate + Actual inflation rate Actual nominal interest rate = \(3\% + 7\% = 10\%\) Now, calculate the total amount Boris has to pay back: Total amount to pay back = Principal + (Principal * Actual nominal interest rate) Total amount to pay back = \(10000 + (10000 * 10\%) = 10000 + 1000 = \$ 11,000\) In this scenario, Boris has to pay back a higher amount compared to the initial agreement based on the expected inflation rate. Therefore, Boris is worse off as he experiences a loss, and Lynn is better off since she gains.

Key concepts

Nominal Interest Rate

The nominal interest rate is the rate agreed upon between a borrower and a lender without adjusting for inflation. It represents the amount a borrower like Boris agrees to pay back on top of the principal loan amount. In the case of Boris and Lynn, the nominal interest rate agreed was 8%. This means Boris would repay the initial $10,000 loan plus an additional 8% of this amount. The nominal rate takes into account both the real interest rate and the expected inflation rate. Essentially, it's a blend of what Lynn hopes to earn from the real interest rate (3% in their agreement) and compensation for the expected loss of purchasing power due to inflation. So, if inflation increases more than expected, the value of the money repaid to Lynn decreases in real terms. Keep this in mind when determining how favorable a loan is for either party. Understanding nominal interest rates is key in analyzing how the financial expectations of borrowers and lenders might shift with changing economic conditions.

Real Interest Rate

The real interest rate provides a more accurate measure of the lender's earnings and the borrower's cost because it accounts for the effects of inflation. In essence, it reflects the actual purchasing power of the interest paid or received. For the loan between Boris and Lynn, the real interest rate was agreed upon as 3%.To find the real interest rate, you can calculate it by subtracting the inflation rate from the nominal interest rate: \[ \text{Real Interest Rate} = \text{Nominal Interest Rate} - \text{Inflation Rate} \]This calculation helps to measure the lender's actual gain once the value of money over time is considered. It's vital for borrowers and lenders as it indicates the true cost of taking or giving a loan. A high real interest rate means loans are more expensive and profitable for lenders, while a low rate indicates cheaper loans for borrowers.

Inflation Rate

Inflation rate is a measure of how much the general level of prices for goods and services rises, thereby eroding purchasing power. It's a crucial factor both for borrowers like Boris and lenders like Lynn, as it affects the real value of borrowed money over time. In the exercise, they expected an inflation rate of 5%. However, the real-world effect is seen distinctly if inflation differs from expectations. If inflation is lower than expected (4%), Lynn's repayment has more purchasing power, but if it is higher (7%), it loses value. This uncertainty introduces risk for both parties, fluctuating their real economic positions depending on the actual inflation rate. When considering loans, both parties tend to agree on a nominal interest rate that foresees expected inflation. Understanding the inflation rate helps adjust expectations around how money's value will change, influencing strategic decisions on borrowing and lending.