Question

A borrower has a 23-year mortgage loan for $464,103 with an interest rate of 6% and monthly payments. If she wants to pay off the loan after 9 years, what would be the outstanding balance on the loan?

Answer 1

The outstanding balance is computed as shown below:

Current monthly payment is computed as follows:

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

r is computed as follows:

= 6% / 12 (Since the payments are on monthly basis, hence divided by 12)

= 0.50% or 0.005

n is computed as follows:

= 23 x 12 (Since the payments are on monthly basis, hence multiplied by 12)

= 276

So, the monthly payment is computed as follows:

$ 464,103 = Monthly payment x [ (1 - 1 / (1 + 0.005)²⁷⁶ ) / 0.005 ]

$ 464,103 = Monthly payment x 149.5109789

Monthly payment = $ 464,103 / 149.5109789

Monthly payment = $ 3,104.139934

Now after 9 years the balance outstanding is computed as follows:

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

n is computed as follows:

= (23 - 9) x 12 (Since the payments are on monthly basis, hence multiplied by 12)

= 168

So, the present value will be computed as follows:

Present value = $ 3,104.139934 x [ (1 - 1 / (1 + 0.005)¹⁶⁸ ) / 0.005 ]

Present value = $ 3,104.139934 x 113.4769898

Present value = $ 352,248.46 Approximately

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