Gracie has an offer to buy an item with a sticker price of $5700 by paying $170 a month for 48 months. Which of these groups of values plugged into the TVM Solver of a graphing calculator will give her the correct answer for the interest rate being offered?
A. $N =4 ; I \%=; PV =-5700 ; PMT =0 ; FV =170 ; P / Y =1 ; C / Y =12 ; PMT : END$
B. $N=4 ; 1 \%=; P V=-5700 ; P M T=0 ; F V=8160 ; P / Y=1 ; C / Y=12 ; P M T: E N D$
C. $N=4 ; 1 \%=; P V=0 ; P M T=-5700 ; F V=170 ; P / Y=1 ; C / Y=12 ; P M T: E N D$
D. $N=4 ; 1 \%=; P V=0 ; P M T=-5700 ; F V=8160 ; P / Y=1 ; C / Y=12 ; P M T: E N D$

To solve this problem, we need to determine which option correctly sets up the Time Value of Money (TVM) Solver for calculating the interest rate in a loan situation.
Gracie is offered a plan to pay $170 every month for 48 months for an item with a sticker price of $5700. We need to solve for the interest rate.
In the context of TVM problems, let's define the terms:

N : The total number of periods (in months here, since she's paying monthly for 48 months, so N = 48 ).

PV (Present Value) : The amount of money that you start with, which is the price of the item here. Gracie is "borrowing" the amount equivalent to the cost of the item at the start, so PV = -5700 because it’s an outflow.

PMT (Payment) : The amount paid per period, which is $170 but considered as outflow in the calculator so it should be negative, PMT = -170 .

FV (Future Value) : The amount of money at the end of the periods, which should be 0 in typical installment loans because you want the balance to be zero. Therefore, FV = 0 .

P/Y (Payments Per Year) : The number of payments per year. Since the payment is monthly, P/Y = 12 .

C/Y (Compounding Periods Per Year) : Typically the same as P/Y in monthly payments, hence C/Y = 12 .


For option analysis, since we're solving for the interest rate I% :

Option A incorrectly sets FV to 170.
Option B incorrectly sets N to 4 and FV to 8160.
Option C sets PV to 0, which is incorrect for a price of $5700.
Option D incorrectly sets PV to 0.

The correct settings for the TVM Solver are as follows:

N = 48
PV = -5700
PMT = -170
FV = 0
P/Y = 12
C/Y = 12
PMT: END

However, none of the given options (A, B, C, or D) accurately provide this setup. It appears this is a mistake in the options provided. Upon review, none of the options are correct based on TVM principles typically taught. Thus, you'll need to input as listed above for accurate results on a graphing calculator TVM Solver.

Answered by RyanHarmon181 | 2025-07-07

None of the provided options are correct for setting up the TVM Solver to calculate the interest rate. The proper values include N=48, PV=-5700, PMT=-170, FV=0, P/Y=12, and C/Y=12. Always ensure that you input the correct values to obtain an accurate interest rate from the TVM Solver.
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Answered by RyanHarmon181 | 2025-07-26