Question

troy took out a loan for $1850 at a 9.6% apr, compounded monthly, to buy a television. if he will make monthly payments of $102.50 to pay off the loan, which of these groups of values plugged into the tvm solver of a graphing calculator could be used to calculate the number of payments he will have to make?

a. n= ; i% = 9.6; pv=-1850; pmt=102.5; fv=0; p/y=1; c/y=12; pmt:end

b. n= ; i% = 0.8; pv=-1850; pmt=102.5; fv=0; p/y=12; c/y=12; pmt:end

c. n= ; i% = 9.6; pv=-1850; pmt=102.5; fv=0; p/y=12; c/y=12; pmt:end

d. n= ; i% = 0.8; pv=-1850; pmt=102.5; fv=0; p/y=1; c/y=12; pmt:end

Explanation:

Step1: Calculate monthly interest rate

The APR is \(9.6\%\). To find the monthly interest rate \(I\), we use the formula \(I=\frac{APR}{12}\). So \(I = \frac{9.6}{12}=0.8\).

Step2: Analyze payment - per - year (\(P/Y\)) and compound - per - year (\(C/Y\))

Since the payments are made monthly, \(P/Y = 12\). And since it is compounded monthly, \(C/Y=12\).

Step3: Analyze present value (\(PV\)), payment (\(PMT\)) and future value (\(FV\))

The loan amount is \(PV=- 1850\) (negative because it's the amount received by the borrower), \(PMT = 102.5\) (positive as it's the amount paid out each month) and \(FV = 0\) (loan is paid off).

Answer:

B. \(N=\) ; \(I\% = 0.8\); \(PV=-1850\); \(PMT = 102.5\); \(FV = 0\); \(P/Y=12\); \(C/Y = 12\); \(PMT:END\)