The table shows a schedule of Jorge's payment plan for a car.
| | Jorge's Payment Plan | | |
| :--- | :------------------------------------ | :---------- | :---------- |
| Year | Balance | Monthly Payment | End of Year Balance |
| 1 | $15,469.80 | $257.83 | |
| 2 | | $257.83 | |
| 3 | | $257.83 | |
| 4 | | $257.83 | |
| 5 | | $257.83 | |
| 6 | | $257.83 | |
How many years will it take Jorge to pay off the loan?
A. 3 years
B. 4 years
C. 5 years
Answer (2)
Jorge will take 5 years to pay off his car loan, as calculated by subtracting his annual payments from the loan balance each year. After performing this calculation step by step, we find that the balance equals zero at the end of Year 5.
;
Calculate the annual payment: A nn u a lP a y m e n t = M o n t h l y P a y m e n t × 12 = $257.83 × 12 = $3093.96 .
Subtract the annual payment from the initial balance for each year.
Continue until the balance is zero or negative.
It will take Jorge 5 years to pay off the loan.
Explanation
Understanding the Problem We are given a table that shows Jorge's payment plan for a car. We need to determine how many years it will take Jorge to pay off the loan, given the initial balance and monthly payment.
Calculating Annual Payment First, we calculate the annual payment by multiplying the monthly payment by 12: A nn u a lP a y m e n t = M o n t h l y P a y m e n t × 12 A nn u a lP a y m e n t = $257.83 × 12 = $3093.96
Calculating End-of-Year Balance Next, we calculate the end-of-year balance for each year by subtracting the annual payment from the beginning balance. We continue this process until the end-of-year balance is less than or equal to zero.
Iterating Through the Years Year 1: Beginning Balance = $15469.80 End-of-Year Balance = Beginning Balance - Annual Payment End-of-Year Balance = $15469.80 - $3093.96 = $12375.84
Year 2: Beginning Balance = $12375.84 End-of-Year Balance = $12375.84 - $3093.96 = $9281.88
Year 3: Beginning Balance = $9281.88 End-of-Year Balance = $9281.88 - $3093.96 = $6187.92
Year 4: Beginning Balance = $6187.92 End-of-Year Balance = $6187.92 - $3093.96 = $3093.96
Year 5: Beginning Balance = $3093.96 End-of-Year Balance = $3093.96 - $3093.96 = $0.00
Determining the Number of Years Since the balance is exactly $0 at the end of Year 5, it will take Jorge 5 years to pay off the loan.
Examples
Understanding loan payment plans is crucial in personal finance. This problem demonstrates how to calculate the time it takes to pay off a loan with fixed monthly payments. This concept applies to various real-life scenarios, such as mortgages, student loans, and credit card debt. By understanding how loan balances decrease over time, individuals can make informed decisions about managing their debt and planning their financial future. For instance, knowing the impact of making extra payments or refinancing a loan can significantly reduce the total repayment time and interest paid.
