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Chapter 4: Problem 10

Lavonda took out a \(\$ 7,500\) loan with an APR of 6.875\(\%\) and agreed to paid it back monthly over six years. How many monthly payments did she make?

Short Answer

Expert verified
Lavonda agreed to make 72 monthly payments.

Step by step solution

01

Understand the payment frequency

First thing to understand is the frequency of payments which is monthly in this case. It means Lavonda will make payments once in every month.
02

Convert Years into Months

As Lavonda will pay back the loan over six years, to find out the total number of payments, these years need to be converted into months. We know that one year has 12 months. So, multiply the 6 years by 12.
03

Calculate Total Number of Payments

After multiplying, we will get the total number of payments that Lavonda agreed to make in order to pay back the loan.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

monthly payments
Understanding monthly payments is crucial when dealing with loans. These payments are fixed amounts that you need to pay every month until the loan is completely paid off.
For a loan with a term of six years, the borrower, like Lavonda, will make payments every month, which means she will pay back the loan over 72 months (as 6 years is equivalent to 72 months).
  • The advantage of monthly payments is that they are predictable, making it easier to plan your budget.
  • Monthly payments typically include both interest and a portion of the principal amount.
  • By consistently making monthly payments, borrowers can build a healthy credit history.
Knowing how to calculate your monthly payment can help ensure that you are prepared for the financial commitment of your loan.
APR calculation
APR stands for Annual Percentage Rate and it's an important measure when considering a loan. It represents the annual cost of borrowing, incorporating the interest rate and any additional fees.
  • APR helps you compare different loan options by showing the true cost of borrowing.
  • In Lavonda's case, her loan APR is 6.875\%, which means that's the annual cost of the loan she needs to repay.
  • To find the monthly rate from the APR, you divide the APR by 12 (the number of months in a year).
The formula to convert APR to a monthly interest rate is as follows: \[ \text{Monthly Interest Rate} = \frac{\text{APR}}{12} \]
This is vital to determine how much interest you will be paying as part of the monthly payments.
loan term in months
The loan term is the duration over which the loan has to be paid back. It is important to convert the loan term into months when calculating monthly payments.
Lavonda鈥檚 loan, for example, is over six years. To determine the loan term in months, we multiply the number of years (6 in this case) by the number of months in a year (12), giving us:
\[ 6 \times 12 = 72 \text{ months} \]
This means Lavonda has agreed to making 72 monthly payments to pay off her loan completely over the term.
Understanding the loan term in months helps you
  • Calculate the total interest paid over the life of the loan.
  • Assess whether the monthly payments are manageable within your budget.
  • Determine how long you will be in debt.
Having a clear understanding of the loan term is essential for making informed financial decisions and ensuring successful loan repayment.

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Most popular questions from this chapter

Jennifer wants to borrow \(\$ 20,000 .\) Her bank offers a 7.1\(\%\) interest rate. She can afford \(\$ 500\) a month for loan payments. What should be the length of her loan to the nearest tenth of a year?

The following inequalities give information on your credit scores. Let \(x\) represent your credit score. \(\bullet\) If \(x>700,\) your credit score is excellent. \(\bullet\) If \(680< x< 700,\) your credit score is good. \(\bullet\) If \(620< x< 680\) , your credit score should be watched carefully. \(\bullet\) If \(580< x< 620\) , your credit score is low \(\bullet\) If \(x< 580,\) your credit score is poor. If Mary Ann's credit score is low, but she receives 40 points for paying off some delinquent debts, is it possible that her credit rating is now good? Explain.

Olivia is considering membership to the Regional Teachers Credit Union so that she can save money on a loan. The credit union will lend her \(\$ 8,000\) for three years at 8.25\(\%\) APR. The same loan at her savings bank has an APR of 10.5\(\% .\) How much would olivia save in finance charges if she joined the credit union and took out her loan there? Round to the nearest ten dollars.

Zea has a credit limit of \(\$ 2,000\) on her credit card. Each month, she charges about \(\$ 200\) and makes a payment of \(\$ 125\) . a. Estimate the number of months that Zea can continue this pattern until she reaches her credit limit. b. Consider that part of the \(\$ 125\) Zea pays each month will be for finance charges. How will the number of months from part a be affected by these charges?

Devon is considering taking out a \(\$ 7,000\) loan. He went to two banks. Stevenson Trust Company offered him an 8 -year loan with an interest rate of 8.6\(\% .\) First National Bank offered him a 5 -year loan with an interest rate of 10\(\% .\) Which loan will have the lower interest over its lifetime?
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