Question

# You have saved \$5,000 for a down payment on a new car. The largest monthly payment...

You have saved \$5,000 for a down payment on a new car. The largest monthly payment you can afford is \$400. The loan will have a 15% APR based on end-of-month payments. What is the most expensive car you can afford if you finance it for 48 months? For 60 months? Do not round intermediate calculations. Round your answers to the nearest cent.

Solution

Most expensive car that can be afforded =Loan amount+Downpayment=

Loan amount =Present value of annuity=Annuity payment*((1-(1/(1+i)^m))/i)

where

i-discount or intrest rate per period-15/12=1.25% per month

m-number of periods

Present value of annuity =?

Annuity payment =400

Finance for 48 months

m=48

Putting values in formula

Loan amount=Present value of monthly payments(Annuity)=400*((1-(1/(1+.0125)^48))/.0125)=14372.59236

Thus the maximum value for which he can afford the car=14372.59236+5000=\$19372.59 (Rounded to nearest cent)

Finance for 60 months

Loan amount=Present value of monthly payments(Annuity)=400*((1-(1/(1+.0125)^60))/.0125)=16813.8367

Thus the maximum value for which he can afford the car=16813.8367+5000=\$21813.84 (Rounded to nearest cent)

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