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QuestionRegina has two car options. Calculate monthly payments for:
1. Car A: \$24,200 at 6.5\% for 11 years.
2. Car B: \$26,000 at 5.3\% for 9 years.

Studdy Solution

STEP 1

Assumptions1. For Ad A, the car costs \$24,200 and the loan has an interest rate of6.5\% per year for11 years. . For Ad B, the car costs \$26,000 and the loan has an interest rate of5.3\% per year for9 years.
3. The interest is compounded annually.
4. The loan is repaid in equal monthly installments over the lifetime of the loan.

STEP 2

First, we need to calculate the monthly interest rate. This can be done by dividing the annual interest rate by12.
Monthly interest rate=Annual interest rate/12Monthly\, interest\, rate = Annual\, interest\, rate /12

STEP 3

Now, plug in the given values for the annual interest rate for Ad A and Ad B to calculate the monthly interest rates.
For Ad AMonthly interest rate=6.5%/12Monthly\, interest\, rate =6.5\% /12For Ad BMonthly interest rate=5.3%/12Monthly\, interest\, rate =5.3\% /12

STEP 4

Convert the percentages to decimal values.
For Ad A6.%=0.0656.\% =0.065Monthly interest rate=0.065/12Monthly\, interest\, rate =0.065 /12For Ad B.3%=0.053.3\% =0.053Monthly interest rate=0.053/12Monthly\, interest\, rate =0.053 /12

STEP 5

Calculate the monthly interest rates.
For Ad AMonthly interest rate=0.065/12=0.00541667Monthly\, interest\, rate =0.065 /12 =0.00541667For Ad BMonthly interest rate=0.053/12=0.00441667Monthly\, interest\, rate =0.053 /12 =0.00441667

STEP 6

Next, we need to calculate the total number of payments. This can be done by multiplying the number of years by12.
Total number of payments=Number of yearstimes12Total\, number\, of\, payments = Number\, of\, years \\times12

STEP 7

Now, plug in the given values for the number of years for Ad A and Ad B to calculate the total number of payments.
For Ad ATotal number of payments=11times12Total\, number\, of\, payments =11 \\times12For Ad BTotal number of payments=9times12Total\, number\, of\, payments =9 \\times12

STEP 8

Calculate the total number of payments.
For Ad ATotal number of payments=11times12=132Total\, number\, of\, payments =11 \\times12 =132For Ad BTotal number of payments=times12=108Total\, number\, of\, payments = \\times12 =108

STEP 9

Now, we can calculate the monthly payment using the formulaMonthly payment=Loan amounttimesMonthly interest ratetimes(+Monthly interest rate)Total number of payments(+Monthly interest rate)Total number of payments−Monthly\, payment = Loan\, amount \\times \frac{Monthly\, interest\, rate \\times ( + Monthly\, interest\, rate)^{Total\, number\, of\, payments}}{( + Monthly\, interest\, rate)^{Total\, number\, of\, payments} -}

STEP 10

Plug in the values for the loan amount, monthly interest rate, and total number of payments for Ad A and Ad B to calculate the monthly payments.
For Ad AMonthly payment=$24,200times0.00541667times(+0.00541667)132(+0.00541667)132−Monthly\, payment = \$24,200 \\times \frac{0.00541667 \\times ( +0.00541667)^{132}}{( +0.00541667)^{132} -}For Ad BMonthly payment=$26,000times0.00441667times(+0.00441667)108(+0.00441667)108−Monthly\, payment = \$26,000 \\times \frac{0.00441667 \\times ( +0.00441667)^{108}}{( +0.00441667)^{108} -}

STEP 11

Calculate the monthly payments.
For Ad AMonthly payment=$24,200times0.00541667times(+0.00541667)132(+0.00541667)132−=$263.26Monthly\, payment = \$24,200 \\times \frac{0.00541667 \\times ( +0.00541667)^{132}}{( +0.00541667)^{132} -} = \$263.26For Ad BMonthly payment=$26,000times0.00441667times(+0.00441667)108(+0.00441667)108−=$301.71Monthly\, payment = \$26,000 \\times \frac{0.00441667 \\times ( +0.00441667)^{108}}{( +0.00441667)^{108} -} = \$301.71Regina would have to pay \$263.26 per month if she bought the car shown in Ad A and \$301.71 per month if she bought the car shown in Ad B.

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