Question

You are thinking about a vintage car that costs $50,000.  The car dealer proposes the following deal: He will lend you the money, and you will repay the loan by making the same payment every three months for the next 20 years (i.e. 80 total payments).  If the interest rate is 6% APR with monthly compounding, how much will you have to pay every three months?

Answer 1

The amount is computed as shown below:

Present value = Quarterly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 6% / 4 (Since the payments are on quarterly basis, hence divided by 4)

= 1.50% or 0.015

n is computed as follows:

= 20 x 4 (Since the payments are on quarterly basis, hence multiplied by 4)

= 80

So, the quarterly payment is computed as follows:

$ 50,000 = Quarterly payment x [ (1 - 1 / (1 + 0.015)⁸⁰ ) / 0.015 ]

$ 50,000 = Quarterly payment x 46.40732349

Quarterly payment = $ 50,000 / 46.40732349

Quarterly payment = $ 1,077.42 Approximately

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