Select The Correct Answer.Regina Has $\$500$ In A Savings Account. She Wants To Purchase A Washer And Dryer Set For $\$1,600$, And She Takes Out An Interest-free Loan At The Store. Her Monthly Payment Is $\$134$. Regina Saves

Understanding the Problem

Regina has a savings account with $\$500$ and wants to purchase a washer and dryer set for $\$1,600$. To finance her purchase, she takes out an interest-free loan at the store with a monthly payment of $\$134$. In this scenario, we need to determine how long it will take Regina to save enough money to pay off the loan and purchase the washer and dryer set.

Calculating the Total Amount Paid

To calculate the total amount paid, we need to multiply the monthly payment by the number of months it will take Regina to pay off the loan. Since Regina has $\$500$ in her savings account, she will need to pay off the remaining amount of $\$1,100$ ($\$1,600$ - $\$500$) through the loan.

Determining the Number of Months

To determine the number of months it will take Regina to pay off the loan, we can use the formula:

Number of months = Total amount / Monthly payment

Plugging in the values, we get:

Number of months = $\$1,100$ / $\$134$ ≈ 8.21 months

Since Regina cannot pay off the loan in a fraction of a month, we will round up to the nearest whole number. Therefore, it will take Regina approximately 9 months to pay off the loan.

Calculating the Total Amount Paid

Now that we know the number of months it will take Regina to pay off the loan, we can calculate the total amount paid:

Total amount paid = Monthly payment x Number of months = $\$134$ x 9 = $\$1,206$

Determining the Remaining Amount

To determine the remaining amount, we need to subtract the total amount paid from the total amount borrowed:

Remaining amount = Total amount borrowed - Total amount paid = $\$1,100$ - $\$1,206$ = -$\$106$

Since the remaining amount is negative, it means that Regina will actually owe the store $\$106$ after paying off the loan.

Conclusion

In conclusion, it will take Regina approximately 9 months to pay off the loan and purchase the washer and dryer set. However, she will actually owe the store $\$106$ after paying off the loan. This is because the monthly payment of $\$134$ is not enough to cover the interest-free loan of $\$1,100$.

Key Takeaways

• Regina will need to pay off the remaining amount of $\$1,100$ through the loan.
• It will take Regina approximately 9 months to pay off the loan.
• Regina will actually owe the store $\$106$ after paying off the loan.

Real-World Applications

This problem can be applied to real-life scenarios where individuals take out loans to purchase large items, such as cars or homes. It is essential to consider the total amount borrowed, the monthly payment, and the number of months it will take to pay off the loan to avoid owing money after paying off the loan.

Mathematical Concepts

This problem involves the following mathematical concepts:

• Multiplication
• Division
• Subtraction
• Addition

These concepts are essential in solving problems involving loans, savings, and financial planning.

Solutions

There are several solutions to this problem, including:

• Regina can increase her monthly payment to pay off the loan faster.
• Regina can consider taking out a loan with a lower interest rate to save money on interest.
• Regina can consider saving more money in her savings account to reduce the amount borrowed.

Conclusion

Frequently Asked Questions

Q: How much money does Regina have in her savings account? A: Regina has $\$500$ in her savings account.

Q: How much does the washer and dryer set cost? A: The washer and dryer set costs $\$1,600$.

Q: How much is Regina's monthly payment? A: Regina's monthly payment is $\$134$.

Q: How long will it take Regina to pay off the loan? A: It will take Regina approximately 9 months to pay off the loan.

Q: Will Regina owe the store any money after paying off the loan? A: Yes, Regina will actually owe the store $\$106$ after paying off the loan.

Q: Why will Regina owe the store money after paying off the loan? A: Regina will owe the store money because the monthly payment of $\$134$ is not enough to cover the interest-free loan of $\$1,100$.

Q: What are some possible solutions to this problem? A: Some possible solutions include:

• Increasing Regina's monthly payment to pay off the loan faster.
• Considering taking out a loan with a lower interest rate to save money on interest.
• Saving more money in Regina's savings account to reduce the amount borrowed.

Q: What are some real-world applications of this problem? A: This problem can be applied to real-life scenarios where individuals take out loans to purchase large items, such as cars or homes.

Q: What mathematical concepts are involved in solving this problem? A: The mathematical concepts involved in solving this problem include:

• Multiplication
• Division
• Subtraction
• Addition

Q: Can Regina avoid owing the store money after paying off the loan? A: Yes, Regina can avoid owing the store money after paying off the loan by increasing her monthly payment, considering taking out a loan with a lower interest rate, or saving more money in her savings account.

Q: How can Regina determine the number of months it will take to pay off the loan? A: Regina can determine the number of months it will take to pay off the loan by using the formula:

Number of months = Total amount / Monthly payment

Q: What is the total amount paid by Regina? A: The total amount paid by Regina is $\$1,206$.

Q: What is the remaining amount after paying off the loan? A: The remaining amount after paying off the loan is $\$106$.

Conclusion

In conclusion, this Q&A article provides answers to frequently asked questions about Regina's savings and loan. The questions cover topics such as the amount of money Regina has in her savings account, the cost of the washer and dryer set, and the number of months it will take Regina to pay off the loan. The answers provide insight into the mathematical concepts involved in solving this problem and offer possible solutions to avoid owing the store money after paying off the loan.