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.

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .