Answer :
To determine which group of values in the TVM Solver will provide the correct answer for the interest rate being offered on Ashton’s loan, let's first set up the problem using the standard variables used in financial calculations:
- [tex]\( N \)[/tex] is the total number of payment periods.
- [tex]\( I\% \)[/tex] is the annual interest rate.
- [tex]\( PV \)[/tex] is the present value or principal of the loan (initial amount borrowed).
- [tex]\( PMT \)[/tex] is the payment made each period.
- [tex]\( FV \)[/tex] is the future value (the remaining balance after all payments are made).
- [tex]\( P/Y \)[/tex] is the number of payments per year.
- [tex]\( C/Y \)[/tex] is the number of compounding periods per year.
- [tex]\( PMT: END \)[/tex] would indicate payments are made at the end of each period (rather than the beginning).
Given the problem:
- Sticker price of the item: \[tex]$4900 (thus, \( PV = -4900 \); the present value of the loan is the negative value because it represents an outflow of money). - Monthly payment: \$[/tex]140 (thus, [tex]\( PMT = 140 \)[/tex]).
- Number of months: 48 (thus, [tex]\( N = 48 \)[/tex]; the number of payments to be made).
Since the payments are monthly, the number of payments per year [tex]\( P/Y \)[/tex] is 12. The number of compounding periods per year [tex]\( C/Y \)[/tex] is also 12, assuming interest is compounded monthly.
The future value [tex]\( FV \)[/tex] of the loan after all the payments are made should be 0, since you're paying off the loan completely.
Now let's analyze the options provided:
A. [tex]\( N = 4; I\% = ?; PV = -4900; PMT = 0; FV = 6720; P/Y = 1; C/Y = 12; PMT: END \)[/tex]
- [tex]\( N \)[/tex] should be 48 (since it's the total number of monthly payments).
- [tex]\( PMT \)[/tex] should be 140 (the monthly payment).
- [tex]\( FV \)[/tex] should be 0 (the loan should be paid off).
- [tex]\( P/Y \)[/tex] should be 12.
Hence, this is not correct.
B. [tex]\( N = 4; I\% = ?; PV = 0; PMT = -4900; FV = 140; P/Y = 1; C/Y = 12; PMT: END \)[/tex]
- [tex]\( PV \)[/tex] should be -4900.
- [tex]\( PMT \)[/tex] should be 140.
- [tex]\( FV \)[/tex] should be 0.
- [tex]\( P/Y \)[/tex] should be 12.
Hence, this is not correct.
C. [tex]\( N = 4; I\% = ?; PV = -4900; PMT = 0; FV = 140; P/Y = 1; C/Y = 12; PMT: END \)[/tex]
- [tex]\( N \)[/tex] should be 48.
- [tex]\( PMT \)[/tex] should be 140.
- [tex]\( FV \)[/tex] should be 0.
- [tex]\( P/Y \)[/tex] should be 12.
Hence, this is not correct.
D. [tex]\( N = 4; I\% = ?; PV = 0; PMT = -4900; FV = 6720; P/Y = 1; C/Y = 12; PMT: END \)[/tex]
- [tex]\( PV \)[/tex] should be -4900.
- [tex]\( PMT \)[/tex] should be 140.
- [tex]\( FV \)[/tex] should be 0.
- [tex]\( P/Y \)[/tex] should be 12.
Hence, this is not correct.
Given the provided question and the facts:
Correct settings should be:
- [tex]\( N \)[/tex] = 48 (number of payments, since the question states 48 months).
- [tex]\( PV \)[/tex] = -4900 (the initial loan amount).
- [tex]\( PMT \)[/tex] = 140 (the amount of each monthly payment).
- [tex]\( FV \)[/tex] = 0 (since the loan is paid off).
- [tex]\( P/Y \)[/tex] = 12 (monthly payments).
- [tex]\( C/Y \)[/tex] = 12 (monthly compounding).
Thus, none of the provided options A, B, C, or D are correct. The correct values needed for the TVM Solver should be (but aren't listed):
[tex]\( N = 48; I\% = ?; PV = -4900; PMT = 140; FV = 0; P/Y = 12; C/Y = 12; PMT: END \)[/tex]
None of the options A, B, C, or D give the correct inputs for solving the rate offered.
- [tex]\( N \)[/tex] is the total number of payment periods.
- [tex]\( I\% \)[/tex] is the annual interest rate.
- [tex]\( PV \)[/tex] is the present value or principal of the loan (initial amount borrowed).
- [tex]\( PMT \)[/tex] is the payment made each period.
- [tex]\( FV \)[/tex] is the future value (the remaining balance after all payments are made).
- [tex]\( P/Y \)[/tex] is the number of payments per year.
- [tex]\( C/Y \)[/tex] is the number of compounding periods per year.
- [tex]\( PMT: END \)[/tex] would indicate payments are made at the end of each period (rather than the beginning).
Given the problem:
- Sticker price of the item: \[tex]$4900 (thus, \( PV = -4900 \); the present value of the loan is the negative value because it represents an outflow of money). - Monthly payment: \$[/tex]140 (thus, [tex]\( PMT = 140 \)[/tex]).
- Number of months: 48 (thus, [tex]\( N = 48 \)[/tex]; the number of payments to be made).
Since the payments are monthly, the number of payments per year [tex]\( P/Y \)[/tex] is 12. The number of compounding periods per year [tex]\( C/Y \)[/tex] is also 12, assuming interest is compounded monthly.
The future value [tex]\( FV \)[/tex] of the loan after all the payments are made should be 0, since you're paying off the loan completely.
Now let's analyze the options provided:
A. [tex]\( N = 4; I\% = ?; PV = -4900; PMT = 0; FV = 6720; P/Y = 1; C/Y = 12; PMT: END \)[/tex]
- [tex]\( N \)[/tex] should be 48 (since it's the total number of monthly payments).
- [tex]\( PMT \)[/tex] should be 140 (the monthly payment).
- [tex]\( FV \)[/tex] should be 0 (the loan should be paid off).
- [tex]\( P/Y \)[/tex] should be 12.
Hence, this is not correct.
B. [tex]\( N = 4; I\% = ?; PV = 0; PMT = -4900; FV = 140; P/Y = 1; C/Y = 12; PMT: END \)[/tex]
- [tex]\( PV \)[/tex] should be -4900.
- [tex]\( PMT \)[/tex] should be 140.
- [tex]\( FV \)[/tex] should be 0.
- [tex]\( P/Y \)[/tex] should be 12.
Hence, this is not correct.
C. [tex]\( N = 4; I\% = ?; PV = -4900; PMT = 0; FV = 140; P/Y = 1; C/Y = 12; PMT: END \)[/tex]
- [tex]\( N \)[/tex] should be 48.
- [tex]\( PMT \)[/tex] should be 140.
- [tex]\( FV \)[/tex] should be 0.
- [tex]\( P/Y \)[/tex] should be 12.
Hence, this is not correct.
D. [tex]\( N = 4; I\% = ?; PV = 0; PMT = -4900; FV = 6720; P/Y = 1; C/Y = 12; PMT: END \)[/tex]
- [tex]\( PV \)[/tex] should be -4900.
- [tex]\( PMT \)[/tex] should be 140.
- [tex]\( FV \)[/tex] should be 0.
- [tex]\( P/Y \)[/tex] should be 12.
Hence, this is not correct.
Given the provided question and the facts:
Correct settings should be:
- [tex]\( N \)[/tex] = 48 (number of payments, since the question states 48 months).
- [tex]\( PV \)[/tex] = -4900 (the initial loan amount).
- [tex]\( PMT \)[/tex] = 140 (the amount of each monthly payment).
- [tex]\( FV \)[/tex] = 0 (since the loan is paid off).
- [tex]\( P/Y \)[/tex] = 12 (monthly payments).
- [tex]\( C/Y \)[/tex] = 12 (monthly compounding).
Thus, none of the provided options A, B, C, or D are correct. The correct values needed for the TVM Solver should be (but aren't listed):
[tex]\( N = 48; I\% = ?; PV = -4900; PMT = 140; FV = 0; P/Y = 12; C/Y = 12; PMT: END \)[/tex]
None of the options A, B, C, or D give the correct inputs for solving the rate offered.
