Answer :
The correct answer is: D. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END. Option A uses annual percentage rate (APR), while option D uses the periodic interest rate (monthly rate). Given that the interest rate is compounded monthly, it's more appropriate to use the periodic interest rate (option D).
To calculate the number of payments Kendra will have to make to pay off the loan, we can use the Time Value of Money (TVM) Solver feature of a graphing calculator. We need to set up the values correctly to solve for the number of payments (N).
Let's go through the options:
A. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
B. N=; I% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
C. N=; 1% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
D. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
Let's analyze each option:
A. This option has the correct annual interest rate (8.4%), correct present value (loan amount), correct payment amount, and correct compounding periods per year. Hence, it's a potential correct option.
B. This option has the interest rate incorrectly set as 0.7%. It should be 8.4%, not 0.7%. Hence, it's incorrect.
C. Similar to option B, this option has the interest rate incorrectly set as 0.7%. Hence, it's incorrect.
D. This option has the correct interest rate (8.4%), correct present value, correct payment amount, and correct compounding periods per year. Hence, it's a potential correct option.
So, options A and D are potential correct options. Both have the correct interest rate and payment amount. The difference lies in how the interest rate is represented: option A uses annual percentage rate (APR), while option D uses the periodic interest rate (monthly rate).
Given that the interest rate is compounded monthly, it's more appropriate to use the periodic interest rate (option D). Therefore, option D is the most suitable choice.
Complete Question:
Kendra took out a loan for $750 at an 8.4% APR, compounded monthly, to buy a stereo. If she will make monthly payments of $46.50 to pay off the loan, which of these groups of values plugged into the TVM Solver of a graphing to make?
A. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
B. N=; I% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
C. N=; 1% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
D. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
Final answer:
To calculate the number of payments for Kendra's loan using a TVM Solver, the correct setup includes an APR of 8.4% converted to a monthly rate of 0.7%, with matching payment and compounding frequencies, making Option A the accurate choice.
Explanation:
When Kendra takes out a loan to buy a stereo, calculating the number of payments she will have to make involves understanding the terms used in Time Value of Money (TVM) calculations. The correct set of values must account for the annual percentage rate (APR) being compounded monthly, which requires converting the APR to a monthly rate, and ensuring the payment and compounding periods match.
For Kendra's loan:
- APR is 8.4%, implying a monthly interest rate (I%) of 0.7% (8.4% divided by 12).
- The present value (PV) of the loan is -$750, indicating an outflow of cash.
- Her monthly payment (PMT) is $46.50, aimed at reducing the loan balance.
- The future value (FV) she aims for is $0, meaning she intends to fully repay the loan.
- P/Y (Payments per year) and C/Y (Compounding periods per year) both should match the monthly nature of the loan, hence should be 12.
Given these conditions, the only option that correctly configures all elements for a TVM Solver is Option A:
N=; I% = 0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
This configuration accurately reflects the loan's terms, allowing the calculation of the number of payments (N) Kendra will need to make.