Questions: A couple wants to buy a 40,000 car and can borrow the money for the purchase at 9%, paying it off in 3,4, or 5 years. The table to the right gives the monthly payment and total cost of the purchase (including the loan) for each of the payment plans. Suppose that when the payment is over t years, P(t) represents the monthly payment and C(t) represents the total cost for the car loan. Use this information to answer parts (a) through (d). t (years) Monthly Payment Total Cost 3 1271.99 45,791.6 4 995.41 47,779.6 5 830.34 49,820.4 a. Find P(5) and write a sentence that explains its meaning. Select the correct choice below and fill in the answer box to complete your choice.

A couple wants to buy a 40,000 car and can borrow the money for the purchase at 9%, paying it off in 3,4, or 5 years. The table to the right gives the monthly payment and total cost of the purchase (including the loan) for each of the payment plans. Suppose that when the payment is over t years, P(t) represents the monthly payment and C(t) represents the total cost for the car loan. Use this information to answer parts (a) through (d).

t (years) Monthly Payment Total Cost
3 1271.99 45,791.6
4 995.41 47,779.6
5 830.34 49,820.4

a. Find P(5) and write a sentence that explains its meaning. Select the correct choice below and fill in the answer box to complete your choice.

Transcript text: A couple wants to buy a $\$ 40,000$ car and can borrow the money for the purchase at $9 \%$, paying it off in 3,4 , or 5 years. The table to the right gives the monthly payment and total cost of the purchase (including the loan) for each of the payment plans. Suppose that when the payment is over $t$ years, $\mathrm{P}(\mathrm{t})$ represents the monthly payment and $\mathrm{C}(\mathrm{t})$ represents the total cost for the car loan. Use this information to answer parts (a) through (d). \begin{tabular}{|c|c|c|} \hline t (years) & \begin{tabular}{c} Monthly \\ Payment \$ \end{tabular} & \begin{tabular}{c} Total \\ Cost \$ \end{tabular} \\ \hline 3 & 1271.99 & $45,791.6$ \\ \hline 4 & 995.41 & $47,779.6$ \\ \hline 5 & 830.34 & $49,820.4$ \\ \hline \end{tabular} a. Find $P(5)$ and write a sentence that explains its meaning. Select the correct choice below and fill in the answer box to complete your choice.

Solution

Solution Steps

To solve this problem, we need to extract the monthly payment for a 5-year loan from the given table and explain its meaning.

Solution Approach

Identify the monthly payment for a 5-year loan from the table.
Write a sentence explaining that this value represents the monthly payment amount for the car loan over a period of 5 years.

Step 1: Identify the Monthly Payment for a 5-Year Loan

From the given table, we extract the monthly payment for a 5-year loan. The table provides the following data: \[ \begin{array}{|c|c|c|} \hline t \, (\text{years}) & \text{Monthly Payment} \, (\$) & \text{Total Cost} \, (\$) \\ \hline 3 & 1271.99 & 45791.6 \\ \hline 4 & 995.41 & 47779.6 \\ \hline 5 & 830.34 & 49820.4 \\ \hline \end{array} \] For $ t = 5 $ years, the monthly payment $ P(5) $ is $ 830.34 $.

Step 2: Explain the Meaning of $ P(5) $

The value $ P(5) = 830.34 $ represents the monthly payment amount for the car loan over a period of 5 years.