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janelle wishes to finance a car for $33,000. the bank's annual interest rate is 3.5%, and she can choose between durations of five or six years. calculate the monthly payment and total amount paid for both duration options.use the formula,p = ar (1+r)^n/(1+r)^n-1where a is the amount to finance, r is the monthly interest rate, and n is the number of months to pay. show all of your steps.

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Answer:

For a duration of 5 years, Monthly Payment =$600.42

For a duration of 6 years, Monthly Payment =$508.83

Step-by-step explanation:

[tex]P=\dfrac{ar (1+r)^n}{(1+r)^n-1} \\[/tex]

where a= Amount to Finance=$33,000

Annual interest rate = 3.5%=0.035

r=Monthly Interest Rate= 0.035 ÷ 12 =[tex]\frac{7}{2400}[/tex]

n=number of months to pay

For a duration of 5 years

n=5X12=60 months

[tex]P=\dfrac{ar (1+r)^n}{(1+r)^n-1} \\\\P=\dfrac{33000 X\frac{7}{2400} (1+\frac{7}{2400} )^{60}}{(1+\frac{7}{2400})^{60}-1} \\=\dfrac{96.25 (1.1909)}{1.1909-1}\\=\dfrac{96.25 (1.1909)}{0.1909}\\=\dfrac{114.62}{0.1909}=\$600.42[/tex]

For a duration of 6 years

n=6X12=72 months

[tex]P=\dfrac{ar (1+r)^n}{(1+r)^n-1} \\\\P=\dfrac{33000 X\frac{7}{2400} (1+\frac{7}{2400} )^{72}}{(1+\frac{7}{2400})^{72}-1} \\=\dfrac{96.25 (1.2333)}{1.2333-1}\\=\dfrac{96.25 (1.2333)}{0.2333}\\=\dfrac{118.71}{0.2333}=\$508.83[/tex]

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