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A friend is selling you a used car. The purchase price is $20,000 and she is...

A friend is selling you a used car. The purchase price is $20,000 and she is providing financing at a friendly 4% annual rate. Because you are currently making tuition payments, she is not requiring the first monthly payment until 2 years from today. After the first payment, you will make 20 more monthly payments of the same amount. If you ave $5,000 to pay today as a down payment, what will your monthly payment be?

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Answer #1

Purchase Price = $ 20000, Immediate Down Payment = $ 5000, Borrowing = 20000 - 5000 = $ 15000

Interest Rate = 4 % per annum and Moratorium (payment deferral) = 2 years or 24 months

Borrowing Value after 2 years = Initial Borrowing + Interest Accumulated = 15000 x (1.04)^(2) = $ 16224

Number of Monthly Payments = 21 and let these payments be worth $ K

Monthly Rate = 4 / 12 = 0.33 %

Therefore, 16224 = K + K x (1/0.0033) x [1-{1/(1.0033)^(20)}]

16224 = K + K x 19.3235

16224 = 20.3235 K

K = 16224 / 20.3235 = $ 798.289 ~ $ 798.29

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