# Math/Finance

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A guy buys a car for \$29,000 and finances it with a four year, 7% APR with monthly payments and compounding. How much of his third payment goes toward repaying principal?

• Math/Finance -

first you need the monthly payment
i = .07/12= .00583333
n = 4(12) = 48
29000 = paym( 1 - 1.00583333^-48)/.00583333
payment = \$694.44

amount owing after 2 payments
= 29000(1.00583333)^2 - 694.44(1.0058333^2 - 1)/.00583333
= 27946.39

interest on that is 163.02
so principal of 3rd payment = 694.44 - 163.02 = 531.42

or, we could set up a chart
payment# paym interest principal balance
...0.....................................................29000.00
...1............694.44..169.17 ..525.27..28474.73
...2............694.44..166.10 ..528.34..27946.39
...3............694.44..163.02 ..531.42..27414.97

notice the principal in the third row is 531.42 , exactly to the penny of the answer to my first method.

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