James purchased a $205,000 home with a 30-year mortgage at 5.78%. if makes a $1500 monthly mortgage payment, how many months early will he pay off his mortgage? a. 180 months b. 224 months c. 127 months d. 136 months

James will pay off his mortgage 136 months early.

Step-by-step explanation:

 Given : Amount to be paid(A)= $205000

Interest rate per annum = 5.78% = 0.0578

monthly interest rate(i) = = 0.004817 (approx)

Monthly payment (P) = $1500.

we have to find how many months early will he pay off his mortgage

We know,  

Substitute values , we get,

Solving for t ,

Applying ln both sides,we get,

Thus, t = 224 months.

1 year = 12 month thus, 30 years = 360 months.

Difference = 360 - 224 = 136 months

Thus, James will pay off his mortgage (360-224) 136 months early.

136 months

Step-by-step explanation:

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step-by-step explanation: