Suppose that you have two alternatives to purchase a new Mini Cooper. You must put $2500 down, and make payments of $387 per month for 48 months, at the end of each month, or pay $19,000 cash. The dealer's stated financing rate is 5.1% APR. If you pay cash for the car, how much money are you saving (+) or losing (-) in comparison with financing your purchase through the dealer? (Your answer should be positive when saving money, negative when you are paying more.)
Present value of montly payments | |||
Present Value Of An Annuity | |||
= C*[1-(1+i)^-n]/i] | |||
Where, | |||
C= Cash Flow per period | |||
i = interest rate per period | |||
n=number of period | |||
= $387[ 1-(1+0.00425)^-48 /0.00425] | |||
= $387[ 1-(1.00425)^-48 /0.00425] | |||
= $387[ (0.1842) ] /0.00425 | |||
= $16,771.67 | |||
Total payment = $2500+16771.67 | |||
=$19271.67 | |||
Cash Alternative = $19000 | |||
You will save = $19271.67-19000 | |||
=$271.67 | |||
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