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A car is for sale at 25000USD. 2000USD will be taken off for cash. For 48 months it can be financed at 2.0 APR or a bank loan obtained for cash at 5.75 APR. Which is the better option?
Wiki User
∙ 8y ago
The monthly repayment can be worked out from:
monthly_payment = Loan × r^n × (r - 1) / (r^n -1)
where n is the number of months
and r is (1 + APR/100)^(1/12)
In this case:
Financing through the dealer:
Loan = $25,000
n = 48
r = (1 + 2/100)^(1/12) = 1.02^(1/12)
monthly_repayment = $25,000 × (1.02^(1/12))^48 × (1.02^(1/12) - 1) / ((1.02^(1/12))^48 - 1) ≈ $542.18
Total repayment is $26,024.64
Total interest is $1,024.64
Financing a cash loan through bank:
Loan = $23,000
n = 48
r = (1 + 5.75/100)^(1/12) = 1.0575^(1/12)
monthly_repayment = $23,000 × (1.0575^(1/12))^48 × (1.0575^(1/12) - 1) / ((1.0575^(1/12))^48 - 1) ≈ $535.99
Total repayment is $25,727.52
Total interest is $2,727.52
Although the total interest in the dealer finance is less, the monthly payments, and hence the total repayments is more. The bank loan is the better option.
Wiki User
∙ 8y ago
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