Question

A couple has just purchased a home for $312,100.00. They will pay 20% down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of 5.64% APR with monthly compounding. The mortgage has a term of 30 years.

What is the size of the loan taken out by the couple?

Answer 1

The size of the loan is computed as shown below:

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

r is computed as follows:

= 5.64% / 12 (Since the payments are monthly, hence divided by 12)

= 0.47% or 0.0047

n is computed as follows:

= 30 x 12 (Since the payments are monthly, hence multiplied by 12)

= 360

So, the monthly payment will be computed as follows:

$ 3,12,100 - 20% = Monthly payment x [ (1 - 1 / (1 + 0.0047)³⁶⁰ ) / 0.0047]

$ 249,680 = Monthly payment x 173.4293113

Monthly payment = $ 249,680 / 173.4293113

Monthly payment = $ 1,439.66 Approximately

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