Question

Over the course of one year, Hometown Bank paid Mary Lee 3 percent interest on a 1,000 dollars deposit and charged Owen's Bakery 8 percent interest on a \(\$ 900\) loan. How much net income did Hometown bank make? Show your calculations.

Short answer

Hometown Bank made a net income of $42.

Step-by-step solution

Calculate Interest Earned from Mary's Deposit

Hometown Bank paid Mary Lee 3% interest on her $1,000 deposit. To find out how much interest the bank paid her, use the formula for simple interest: \( \, \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \, \). Here, \( \text{Principal} = 1000 \,\), \( \text{Rate} = 0.03 \,\), and \( \text{Time} = 1 \,\text{year} \). So, the interest paid to Mary Lee is: \( 1000 \times 0.03 \times 1 = 30 \,\text{dollars} \).

Calculate Interest Charged to Owen's Bakery

Hometown Bank charged Owen's Bakery 8% interest on their $900 loan. Using the same simple interest formula: \( \, \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \, \). Here, \( \text{Principal} = 900 \,\), \( \text{Rate} = 0.08 \,\), and \( \text{Time} = 1 \,\text{year} \). So, the interest charged to Owen's Bakery is: \( 900 \times 0.08 \times 1 = 72 \,\text{dollars} \).

Calculate Net Income for Hometown Bank

Net income for the bank is the difference between the interest earned from loans and the interest paid on deposits. From Step 1, the bank paid \( 30 \,\text{dollars} \) to Mary Lee, and from Step 2, it earned \( 72 \,\text{dollars} \) from Owen's Bakery. Therefore, the net income is: \( 72 - 30 = 42 \,\text{dollars} \).

Key concepts

Understanding Interest Rates

Interest rates determine how much money needs to be paid or received when borrowing or lending. When you deposit money in a bank, such as Mary did, the bank pays you interest for using your money. On the other hand, when you take a loan, like Owen's Bakery, the bank charges you interest.
Interest rates are typically expressed as a percentage of the principal, which is the amount of money on which the interest is applied. This percentage can be a fixed rate, which stays the same throughout the term, or a variable rate, which can change.

• A lower interest rate on savings means less earning on deposits.
• Conversely, a higher interest rate on loans means more cost for borrowing.

Understanding interest rates is crucial in making financial decisions, whether it's choosing the best savings account or evaluating the cost of a loan.

Banking and Finance Basics

Banking and finance are all about managing money for different needs and operations. Banks play a central role by connecting depositors and borrowers. This is demonstrated in our exercise where Mary deposits money, and Owen's Bakery takes a loan.
Banks function by attracting deposits and offering loans, using the difference in interest rates to generate profit.

• Deposits are pooled together to provide the capital for loans.
• The bank earns by charging more interest on loans than it pays on deposits.

A bank's net income, as calculated in the exercise, shows the profitability of these transactions. Enhancing understanding of these concepts helps in better financial planning and decision-making.

Simple Loan Calculations

Let's dig into simple loan calculations, as showcased in the exercise. Simple interest is one straightforward way to calculate how much extra you pay or earn.
The formula to calculate simple interest is: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] Here's how it works:

• The **Principal** is the original sum of money. In Owen's case, this is \(900\) dollars.
• The **Rate** is expressed as an annual percentage and indicates how much interest is applied. Owen pays 8% interest.
• The **Time** usually refers to the annual period over which the interest is calculated, here, 1 year.

By using simple formulas, anyone can calculate the cost of borrowing or the earning on investments, making it a useful skill in personal finance management.