A consumer makes a $400 down payment on a television that costs $1,570. Which of the following is the number of months it will take to pay off the television with monthly payments of $100? (Assume that no interest is owed)
A.
12
B.
16
C.
15
D.
11
The correct answer and Explanation is :
To determine the number of months it will take to pay off the television, follow these steps:
- Calculate the Remaining Balance:
- The total cost of the television is $1,570.
- The consumer has made a down payment of $400.
- Therefore, the remaining balance is calculated as follows: [
\text{Remaining Balance} = \text{Total Cost} – \text{Down Payment}
] [
\text{Remaining Balance} = 1,570 – 400 = 1,170
]
- Calculate the Number of Months Needed:
- The consumer plans to make monthly payments of $100.
- To find out how many months it will take to pay off the remaining balance, use the formula: [
\text{Number of Months} = \frac{\text{Remaining Balance}}{\text{Monthly Payment}}
] [
\text{Number of Months} = \frac{1,170}{100} = 11.7
] - Since the number of months must be a whole number, round up to the nearest whole number because the consumer would need to make a partial payment in the final month. Thus, 11.7 months rounds up to 12 months.
Explanation:
- Remaining Balance Calculation:
Subtracting the down payment from the total cost gives the amount that still needs to be paid. Here, $1,570 (total cost) – $400 (down payment) = $1,170. - Monthly Payment Calculation:
Dividing the remaining balance by the monthly payment amount tells us how many full payments are required. Here, $1,170 divided by $100 equals 11.7. Since payments are made in full months, you need to round up to 12 months to cover the full amount.
Answer: The number of months it will take to pay off the television is 12 months (option A).