Answered

Which of these groups of values plugged into the TVM Solver of a graphing calculator will give the monthly payment for a 30-year loan for [tex][tex]$\$[/tex] 265,000$[/tex] at [tex]5.9 \%[/tex] interest, compounded monthly?

A. [tex]N = 360 ; I\% = 5.9 ; PV = -265000 ; PMT = ; FV = 0 ; P/Y = 12 ; C/Y = 12 ;[/tex] PMT:END
B. [tex]N = 360 ; I\% = 5.9 ; PV = -265000 ; PMT = ; FV = 0 ; P/Y = 12 ; C/Y = 12 ;[/tex] PMT:END
C. [tex]N = 360 ; I\% = 5.9 ; PV = 0 ; PMT = ; FV = -265000 ; P/Y = 12 ; C/Y = 12 ;[/tex] PMT:END
D. [tex]N = 30 ; I\% = 5.9 ; PV = 0 ; PMT = ; FV = -265000 ; P/Y = 12 ; C/Y = 12 ;[/tex] PMT:END



Answer :

GinnyAnswer
To determine which group of values should be used in the TVM (Time Value of Money) Solver on a graphing calculator to find the monthly payment for a 30-year loan of \$265,000 at 5.9% interest, compounded monthly, we need to analyze each provided group of values carefully.

Let's examine each group:

Group A:
- [tex]\( N = 30 \)[/tex] (incorrect since it should be in months and not years)
- [tex]\( I\% = 5.9 \)[/tex]
- [tex]\( PV = -265000 \)[/tex] (correct, it's the present value or loan amount)
- [tex]\( PMT \)[/tex] (this is what we're solving for, so it's correct that it's left blank)
- [tex]\( FV = 0 \)[/tex] (correct, the future value is zero when the loan is fully paid off)
- [tex]\( P/Y = 12 \)[/tex] (payments per year, correct for monthly payments)
- [tex]\( C/Y = 12 \)[/tex] (compounding periods per year, correct for monthly compounding)
- PMT: END (correct, payments are typically at the end of the period)

Group B:
- [tex]\( N = 360 \)[/tex] (correct since 30 years × 12 months = 360 months)
- [tex]\( I\% = 5.9 \)[/tex]
- [tex]\( PV = -265000 \)[/tex]
- [tex]\( PMT \)[/tex]
- [tex]\( FV = 0 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END

Group C:
- [tex]\( N = 360 \)[/tex]
- [tex]\( I\% = 5.9 \)[/tex]
- [tex]\( PV = 0 \)[/tex] (incorrect, PV should be the loan amount, -265000)
- [tex]\( PMT \)[/tex]
- [tex]\( FV = -265000 \)[/tex] (incorrect, the future value should be zero when the loan is paid off)
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END

Group D:
- [tex]\( N = 30 \)[/tex] (incorrect, see Group A)
- [tex]\( I\% = 5.9 \)[/tex]
- [tex]\( PV = 0 \)[/tex] (incorrect, see Group C)
- [tex]\( PMT \)[/tex]
- [tex]\( FV = -265000 \)[/tex]
- [tex]\( P/Y = 12 \)[/tex]
- [tex]\( C/Y = 12 \)[/tex]
- PMT: END

Conclusion:
Group B provides the correct values that align with what is required to solve for the monthly payment using the TVM Solver, as it correctly converts the 30 years into 360 months for [tex]\( N \)[/tex] and sets the present value [tex]\( PV \)[/tex] to the loan amount (-265000), future value [tex]\( FV \)[/tex] to zero, payment periods and compounding periods per year [tex]\( P/Y \)[/tex] and [tex]\( C/Y \)[/tex] to 12, and specifies payments at the end [tex]\( PMT: END \)[/tex].

Thus, the correct group of values is:

B. [tex]\( N = 360; I\% = 5.9; PV = -265000; PMT = ; FV = 0; P/Y = 12; C/Y = 12; PMT: END \)[/tex]