The Taylors have purchased a $270,000 house. They made an initial down payment of $10,000 and secured a mortgage with interest charged at the rate of 5%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make?

$14,028  

Explanation:

To calculate the monthly payment Taylor will be required to pay, we use loan amortization formula stated as follows:

P = {A × [r(1 + r)^n]} ÷ {[(1+r)^n]-1} (1)

Where,

P = Monthly required payment = ?

A = Loan balance = Loan amount - Initial down payment

   = $270,000 - $10,000 = $260,000

r = interest rate = 5% per year = 0.05 pear year  

 = (0.05 ÷ 12) per month =  0.0042 per year

n = number of payment period = 30 years

  = (30 × 12) months = 360 months  

Substituting values into equation (1), we have:

P = {2,600,000 × [0.0042(1 + 0.0042)^360]} ÷ {[(1+0.0042)^360] - 1}  

  = {2,600,000 × [0.0042(1.0042)^360]} ÷ {[(1.0042)^360] - 1}

  = {2,600,000 × [0.0042 × 4.5215]} ÷ {4.5215 - 1}

  = {2,600,000 × 0.0190} ÷ {3.5215}

  = 49,400 ÷ 3.5215

P = $14,028  

Therefore, Taylor will be required to make a monthly payment of $14,028 for 30 years.

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