Question

Derek decides to buy a new car. The dealership offers him a choice of paying $583.00 per month for 5 years (with the first payment due next month) or paying some amount today. He can borrow money from his bank to buy the car. The bank requires a 5.00% interest rate. What is the most that he would be willing to pay today rather than making the payments?

Answer #1

Equated Monthly Installment (EMI)

= P x R x (1 + R) ^ n / [ (1 + R) ^ n – 1]

Where,

EMI = $583

P = Principal Amount

R = Monthly interest

= Yearly interest / 12

= 5 / 12

= 0.4167% or 0.004166

n = Number of monthly installments

= Number of years x 12

= 5 x 12

= 60

So, putting the values in above equation we get

583 = P x 0.004166 x (1.004166 ^ 60) / [(1.004166 ^ 60 – 1)]

So, 583 = P x 0.005347 / 0.283359

So, P = 583 / 0.018871

**=** $30,893.58

So, the amount which Derek would be willing to pay today is $30,893.58

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