Please help

Question

A couple buys a $170000 home, making a down payment of 18%. The couple finances the purchase with a 15-year mortgage at an annual rate of 2.75%. Find the monthly payment. If the couple decides to increase the monthly payment to $1000, find the number of payments

Answer 1

If the price of the home is $170,000 and they make an 18% down payment, then that downpayment is $30,600, leaving a mortgage of 139,400.

 

To calculate the payment needed

 

M = Pr((1+r)ⁿ

      ----------

       (1+r)ⁿ-1

 

P = 139400 = mortgage amount

r =  .0275/12 = .00229167 = rate which is the interest rate divided by 12, assuming monthly payments

n =  15x12 = 180 = length of loan times 12

 

M = (139400)(.00229167)(1.00229167)¹⁸⁰

      -------------------------------------------

             (1.00229167)¹⁸⁰ -1

 

Working this through, we have

M = $ 946  monthly payment

 

Now if you rounded up the payment to $1000, you would shorten the length of the mortgage.

Use the same formula, with M as the $1000 payment and solve for n.

Remember you will need to use logs to solve for n and that will be the number of months.  Divide by 12 to get the number of years.