The table shows a schedule of Inga's payment plan for a car.
| Year | Balance | Monthly Payment | End of Year Balance |
|---|---|---|---|
| 1 | $19,691.28 | $273.49 | $16,409.40 |
| 2 | $16,409.40 | $273.49 | $13,127.52 |
| 3 | $13,127.52 | $273.49 | $9,845.64 |
How many more years will it take Inga to pay off the loan?
Answer (2)
Inga has approximately 3 more years to pay off her car loan based on her payment plan. By calculating the annual payment from her monthly installments, we determined the remaining balance can be settled in roughly 3 years. This assumes consistent payments without additional interest changes.
;
Calculate the annual payment: $273.49 \times 12 = $3281.88.
Determine the principal reduction each year: approximately $3281.88.
Divide the remaining balance by the annual principal reduction: $\frac{$9,845.64}{ 3281.88} = 3 .
It will take Inga 3 more years to pay off the loan.
Explanation
Understanding the Problem We are given a table showing Inga's payment plan for a car over the first 3 years. We need to determine how many more years it will take Inga to pay off the loan.
Calculate Annual Payment First, let's calculate the annual payment. The monthly payment is 273.49 , so t h e ann u a lp a y m e n t i s : $273.49 \times 12 = 3281.88 $
Calculate Annual Interest and Principal Reduction Next, we need to find the interest paid each year. We can calculate this by subtracting the end-of-year balance from the beginning balance and then subtracting the annual payment. However, since the end-of-year balance already reflects the interest and principal paid, we can approximate the principal reduction each year by the annual payment minus the interest. Since the interest values calculated are negligible, we can assume that the annual payment is approximately equal to the principal reduction.
Calculate Principal Reduction for Each Year Year 1: Beginning balance: $19,691.28 End balance: $16,409.40 Principal reduction: $19,691.28 - $16,409.40 = $3281.88 Year 2: Beginning balance: $16,409.40 End balance: $13,127.52 Principal reduction: $16,409.40 - $13,127.52 = $3281.88 Year 3: Beginning balance: $13,127.52 End balance: $9,845.64 Principal reduction: $13,127.52 - $9,845.64 = $3281.88
Calculate Remaining Years The principal reduction is the same each year, which is $3281.88. Now, we need to determine how many years it will take to pay off the remaining balance of $9,845.64. We can do this by dividing the remaining balance by the annual principal reduction: \frac{$9,845.64}{$3281.88} = 3
Final Answer Therefore, it will take Inga 3 more years to pay off the loan.
Examples
Understanding loan amortization is crucial in personal finance. This problem demonstrates how calculating annual payments and principal reduction helps determine the time required to pay off a loan. For instance, when planning to buy a house or a car, knowing these calculations allows you to estimate the repayment period and adjust your budget accordingly. It also helps in comparing different loan offers to choose the most favorable terms, ensuring you can manage your finances effectively and avoid long-term debt issues.
