Question

Kaitlin has \(\$ 10,000\) of savings that she may deposit with her local bank. Kaitlin wants to earn a real rate of return of at least 4 percent and she is expecting inflation to be exactly 3 percent. What is the lowest nominal interest rate that Kaitlin would be willing to accept from her local bank? a. 4 percent. b. 5 percent. c. 6 percent. d. 7 percent.

Short answer

Kaitlin would accept a nominal interest rate of at least 7 percent.

Step-by-step solution

Understanding the Relationship

The nominal interest rate is the sum of the real interest rate and the expected inflation rate. This can be expressed with the formula: \[ i = r + ext{inflation}\], where \(i\) is the nominal interest rate, \(r\) is the real interest rate, and "inflation" is the expected inflation rate.

Substituting Known Values

Insert the values given in the problem into the formula. Kaitlin wants a real interest rate \( r \) of at least 4 percent, and she expects inflation to be 3 percent. Substitute these values into the formula:\[i = 4\% + 3\%\]

Calculating the Nominal Interest Rate

Perform the addition to find the nominal interest rate:\[i = 7\%\]

Interpreting the Result

The result indicates that Kaitlin would need at least a 7% nominal interest rate in order to achieve her desired real return of 4%, given the expected inflation rate.

Key concepts

Real Interest Rate

The real interest rate gives us an idea of the true return on investment after adjusting for inflation. It's the rate of growth of purchasing power derived from an investment. For example, if Kaitlin wishes to increase her purchasing power by 4%, her real interest rate target must also be 4%. The real interest rate is what effectively improves your financial situation over time.
This becomes crucial in assessing the wellbeing of any investment choice, as it reflects the actual increase in value. To calculate the real interest rate:

• Consider the nominal interest rate as the starting point. This is the advertised interest rate on investments or savings accounts.
• Subtract the expected inflation rate. Inflation reduces the value of money over time, so it needs to be accounted for.

By accounting for inflation, Kaitlin can ensure that her investments truly increase her buying power over time.

Expected Inflation Rate

Expected inflation is a prediction of how much prices will rise in the future. It's a vital factor in determining how much nominal interest an investment must earn to maintain real value. For Kaitlin, expected inflation is 3%. This number helps her to adjust her financial expectations. When dealing with savings or investments:

• Understand that inflation decreases the purchasing power of money. This means a dollar today won't buy as much in the future.
• Use this rate to adjust the nominal interest rate you seek, ensuring you're not just breaking even or losing money effectively.

By taking expected inflation into account, Kaitlin can better protect her savings against the erosion of value over time.

Financial Decision-making

Smart financial decisions often rely on understanding how interest rates, including nominal and real interest rates, affect potential returns. Kaitlin is making a financial decision about her savings. She has a goal to earn a real return of 4% despite expected inflation. Here's how she can approach financial decision-making effectively:

• Identify your financial goals, like Kaitlin's 4% real return.
• Consider external factors like inflation, which will impact your savings.
• Calculate the nominal interest rate required to meet your real return desires while accounting for inflation.

Effective decision-making leads to selecting the best savings or investment options that make the most economic sense given the circumstances.

Interest Rates

Interest rates represent the cost of borrowing money or the reward for saving. Nominal interest rates, as offered by banks or financial institutions, include both the real interest and expected inflation rates. For Kaitlin, the key to understanding interest rates lies in how they influence the growth of her savings. Key points to consider include:

• The nominal interest rate is the headline rate proposed by banks, which incorporates inflation expectations.
• Real interest rates are the genuine return after accounting for inflation.
• Determining the suitable nominal interest rate (minimum of 7% for Kaitlin) ensures her real return meets her expectations.

Grasping the intricacies of interest rates aids Kaitlin in negotiating better deals with banks, thereby maximizing her financial gains.