Question

Suppose you have accumulated a credit card balance of \(\$ 500\), at an annual interest rate of 10 percent. You are also planning to open a new savings account that accumulates interest at an annual rate of 3 percent. You just got your paycheck and have \(\$ 200\) that you can use either to pay down your debt or open your savings account. [LO 8.4] a. If you use the full \(\$ 200\) to pay down your debt, what will your credit card balance be in one year? Assume no additional credit card payments during this time. b. If, instead, you put the full \(\$ 200\) into your savings account, what will be the balance in your savings account in one year, assuming you make no additional deposits during this time? What will your credit card balance be, assuming you make no additional payments during this time because your payment requirements have been deferred for one year? c. In one year, how much money will you have lost if you deposit the \(\$ 200\) in your savings account compared to paying down your credit card?

Short answer

By saving, you lose $14 compared to paying down the debt.

Step-by-step solution

Calculate New Credit Card Balance after Payment

First, let's determine what happens if you pay the entire \(200 towards your credit card debt. Subtract \)200 from the initial balance of \(500: \[ 500 - 200 = 300 \]This leaves you with a balance of \)300. Now, we need to apply the interest to this balance over one year. The interest rate is 10%, so: \[ 300 \times 0.10 = 30 \]Add this interest to the remaining balance to get the total balance after one year: \[ 300 + 30 = 330 \] Thus, your credit card balance in one year will be $330.

Determine Savings Account Balance After One Year

If you deposit the \(200 into the savings account, we'll calculate the end balance after one year with a 3% interest rate.Calculate the interest gained: \[ 200 \times 0.03 = 6 \]Add this interest to your initial savings deposit: \[ 200 + 6 = 206 \]Your savings account will have \)206 after one year.

Calculate Credit Card Balance Without Payment

If you put \(200 into savings instead of paying down the credit card, the credit card interest is applied to the initial balance of \)500 at 10% interest rate. First, calculate the interest:\[ 500 \times 0.10 = 50 \]Add this interest to the initial balance:\[ 500 + 50 = 550 \]Thus, your credit card balance in one year will be $550.

Compute Financial Impact of Savings Choice

We compare the financial outcomes of the two choices. Had you applied the \(200 to the debt, your credit balance would have been \)330. By choosing to save instead, your debt grows to \(550 and your savings balance is \)206. The total effective loss in terms of your overall financial picture is calculated by the additional debt:\[ 550 - 330 = 220 \]Then factor in your savings balance:\[ 220 - 206 = 14 \]Therefore, by putting the money into savings rather than paying down the credit card, you effectively lose an additional $14 in a year's time.

Key concepts

Interest Rates

Interest rates play a significant role in personal finance decision-making. They determine the cost of borrowing money and the returns on investments over time.
For credit cards, an interest rate is applied to the remaining balance, which increases the total debt if not paid off promptly.
In our exercise, a 10% interest rate on the remaining credit card balance after partial payment results in increased debt. This illustrates how the compounding effect of interest can escalate debt over time.
On the other hand, when applied to savings accounts, interest rates allow the saved money to grow. A 3% rate, while comparatively lower, still increases the initial deposit over time.
Understanding different interest rates is essential for smart financial decision-making and striking a balance between debt management and savings growth. Ultimately, higher interest rates on debt compared to savings highlight the importance of prioritizing debt repayment to reduce financial burden.

• For debts, the interest rate adds to what you owe.
• For savings, the rate boosts your growth over time.
• Comparing rates helps in making money-smart decisions.

Credit Card Debt Management

Effective credit card debt management is crucial for maintaining financial health.
When dealing with credit card debt, it's important to actively manage and reduce your balance to minimize interest charges.
In the given scenario, paying down the credit card debt helps to decrease the balance on which interest is calculated.
For example, paying $200 off a $500 debt reduces the interest-bearing balance, thereby decreasing future interest owed. Proper debt management not only helps to minimize financial costs but also improves credit scores, providing future benefits.
Strategies for managing credit card debt include:

• Pay more than the minimum payment each month.
• Focus on paying off the card with the highest interest rate first.
• Consider consolidating debt with a lower-interest loan.

By understanding and applying these strategies, you can effectively reduce credit card debt and prevent it from becoming an overwhelming financial burden.

Savings Account Growth

Growth in a savings account is a key component of personal finance management.
By depositing money into a savings account, you can start earning interest, contributing to the growth of your initial amount over time.
In our scenario, placing $200 into a savings account with a 3% annual interest rate results in a gain of $6 over one year.
This might seem modest, but over time, with additional contributions and compound interest, savings can significantly increase.
Building a savings habit is important for future financial security. It provides a safety net for unexpected expenses and helps achieve long-term goals.
To maximize savings account growth, consider these practices:

• Automate monthly transfers to your savings account.
• Look for accounts offering competitive interest rates.
• Regularly review and adjust your savings goals.

Understanding how savings work and adopting smart saving strategies can help create a solid financial foundation for the future.