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Ashton has an offer to buy an item with a sticker price of [tex]$\$ 4900$[/tex] by paying [tex]$\[tex]$ 140$[/tex][/tex] a month for 48 months. Which of these groups of values plugged into the TVM Solver of a graphing calculator will give him the correct answer for the interest rate being offered?

A. [tex]N = 48[/tex]; [tex]I\% = ?[/tex]; [tex]PV = -4900[/tex]; [tex]PMT = 140[/tex]; [tex]FV = 0[/tex]; [tex]P/Y = 12[/tex]; [tex]C/Y = 12[/tex]; [tex]PMT: END[/tex]
B. [tex]N = 48[/tex]; [tex]I\% = ?[/tex]; [tex]PV = 0[/tex]; [tex]PMT = -140[/tex]; [tex]FV = 4900[/tex]; [tex]P/Y = 12[/tex]; [tex]C/Y = 12[/tex]; [tex]PMT: END[/tex]
C. [tex]N = 48[/tex]; [tex]I\% = ?[/tex]; [tex]PV = -4900[/tex]; [tex]PMT = 0[/tex]; [tex]FV = 6720[/tex]; [tex]P/Y = 12[/tex]; [tex]C/Y = 12[/tex]; [tex]PMT: END[/tex]
D. [tex]N = 48[/tex]; [tex]I\% = ?[/tex]; [tex]PV = 0[/tex]; [tex]PMT = -140[/tex]; [tex]FV = 4900[/tex]; [tex]P/Y = 12[/tex]; [tex]C/Y = 12[/tex]; [tex]PMT: END[/tex]



Answer :

GinnyAnswer
In order to identify the correct group of values to input into the TVM (Time Value of Money) solver of a graphing calculator, let's break down the problem step-by-step:

1. Understanding the Terms and Definitions:
- N: Total number of payments.
- I%: Interest rate per period.
- PV: Present Value (the current amount of money, which in this case is the loan amount).
- PMT: Payment per period (monthly payment).
- FV: Future Value (the amount of money expected in the future).
- P/Y: Payments per year.
- C/Y: Compounding periods per year.
- PMT: END or BGN: When the payment is made (at the end or beginning of each period).

2. Details of Ashton's Offer:
- Sticker price of the item: \[tex]$4900. - Monthly payment: \$[/tex]140.
- Duration: 48 months.

3. Calculating Total Amount Paid:
[tex]\[ \text{Total amount paid} = 140 \, \text{per month} \times 48 \, \text{months} = 6720 \, \text{dollars} \][/tex]

4. TVM Values:
- N (Total number of payments): [tex]\(48\)[/tex] (since payments are monthly for 48 months).
- PV (Present Value): [tex]\(-4900\)[/tex] (it is a liability, hence negative).
- PMT (Payment per month): [tex]\(\$140\)[/tex] (monthly payment).
- FV (Future Value): [tex]\(6720\)[/tex] (the total amount paid by the end of the term).
- P/Y (Payments per Year): [tex]\(12\)[/tex] (monthly payments, so 12 payments per year).
- C/Y (Compounding per Year): [tex]\(12\)[/tex] (interest compounded monthly).

5. Correct Option Analysis:
- Let's match the options with the values we need:
- Option A: Doesn't make sense as PMT and FV are not aligned with the problem details.
- Option B: Correctly has [tex]\( N = 48 \)[/tex], [tex]\( PV = -4900 \)[/tex], [tex]\( PMT = 140 \)[/tex], [tex]\( FV = 6720 \)[/tex], [tex]\( P/Y = 1 \)[/tex], [tex]\( C/Y = 12 \)[/tex], and payments at the end of the period.
- Option C and D: Have incorrect arrangements and values.

Given the detailed breakdown of Ashton's payment plan and the correct TVM solver values, Option B is the correct input group for solving the interest rate being offered.

So, the correct answer is:
[tex]\[ \boxed{\text{B}} \][/tex]

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