Question

Jamie is saving for a trip to Europe. She has an existing savings account that earns 2 percent interest and has a current balance of \(\$ 4,500\). Jamie doesn't want to use her current savings for vacation, so she decides to borrow the \(\$ 1,500\) she needs for travel expenses. She will repay the loan in exactly one year. The annual interest rate is 5 percent. \([\mathrm{LO} 8.4]\) a. If Jamie were to withdraw the \(\$ 1,500\) from her savings account to finance the trip, how much interest would she forgo? b. If Jamie borrows the \(\$ 1,500\), how much will she pay in interest? c. How much does the trip cost her if she borrows rather than dips into her savings?

Short answer

Jamie forgoes $30 in savings interest, pays $75 in loan interest, costing her $45 more to borrow.

Step-by-step solution

Calculate Forgone Interest on Savings

If Jamie withdraws \(1,500 from her savings account, she won't earn interest on that amount for one year. The forgone interest is calculated as follows:\[ \text{Forgone Interest} = \text{Withdrawn Amount} \times \text{Interest Rate} = 1500 \times 0.02 = \\)30 \]

Calculate Loan Interest

Jamie is borrowing \(1,500 at a 5% interest rate to be repaid in one year. The interest on the loan is calculated as follows:\[ \text{Loan Interest} = \text{Loan Amount} \times \text{Interest Rate} = 1500 \times 0.05 = \\)75 \]

Calculate Total Additional Cost of Borrowing

By borrowing for the trip instead of using her savings, Jamie will pay an additional cost, which is the difference between the loan interest and the forgone savings interest:\[ \text{Additional Cost} = \text{Loan Interest} - \text{Forgone Interest} = 75 - 30 = \$45 \]

Key concepts

Forgone Interest

Have you ever thought about what happens to the interest you might "lose" when you withdraw money from your savings to spend it elsewhere? That's what forgone interest is all about. When Jamie considers using her savings for her trip, she must think about how much interest she misses out on by doing so. Forgone interest is essentially the amount of money your savings could have earned, had you not spent it. To compute forgone interest, you simply multiply the amount you would withdraw by the interest rate of the savings account. If Jamie took out \(1,500 from her savings account, she wouldn't earn interest on that portion, calculating as:- Withdrawn Amount: \)1,500- Savings Interest Rate: 2%Thus, her forgone interest would be \(1,500 \times 0.02 = \)30.This missed opportunity to earn $30 is something to factor into financial planning since every bit counts when trying to grow your savings.

Loan Interest

When Jamie borrows money, she needs to understand the concept of loan interest, which is the cost of using the borrowed funds. Lenders charge borrowers an interest rate, which is a percentage of the loan amount, for the privilege of accessing their money. In Jamie’s case, the loan amount she needs is \(1,500, and the interest rate she's being charged is 5% annually.Calculating loan interest is straightforward:- Loan Amount: \)1,500- Loan Interest Rate: 5%The equation for finding the interest amount she needs to repay in a year is \(1,500 \times 0.05 = \)75.Loan interest is more than just a simple number. It’s important because it affects how much you will have to repay over the lifetime of the loan. For Jamie, this means her trip will cost \(75 more than the initial \)1,500 planned because of the interest she'll owe. Understanding this can help in budgeting and making well-informed financial decisions.

Opportunity Cost

Opportunity cost is a key concept in economics that revolves around the idea of making choices and dealing with the trade-offs. For Jamie, the opportunity cost involves deciding between using her savings and paying interest on a loan. It's essentially what she sacrifices when choosing one financial option over another. By deciding to borrow money instead of using savings, Jamie's opportunity cost is the forgone interest of $30 and the $75 loan interest she has to pay. The real cost of her trip isn't just the amount spent but also the additional costs due to her choice: - Forgone Interest: $30 - Loan Interest: $75 Understanding opportunity costs empowers individuals to make decisions that align with their priorities. Perhaps Jamie values keeping her savings intact, seeing the benefit of having them for emergencies more significant than the cost of the loan. Each scenario offers lessons on evaluating financial decisions based on what you're willing to give up.

Savings vs. Borrowing

Savings versus borrowing is a common dilemma for everyone, especially when large expenses come into play, like Jamie's trip to Europe. Each has its pros and cons. When deciding between using savings or borrowing, consider the following:

• Savings: Using savings means avoiding debt. However, doing so means you will miss out on earning interest on those savings because the funds are no longer in your account.
• Borrowing: While borrowing keeps your savings intact, it comes with the cost of interest payments. In Jamie's scenario, choosing to borrow incurs a $75 loan interest cost.

For Jamie, borrowing means her trip costs $45 more than using savings, considering both forgone interest and loan interest. The decision hinges on whether keeping her savings for other purposes or emergencies feels more valuable than paying extra for the loan. This decision-making process is crucial in both personal finance and broader economic concepts, teaching us the importance of weighing immediate benefits against long-term financial implications.