Help please!

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.

 

I got the first part which is= 946.00

 

I am struggling with the second part how to solve for N? 

Answer 1

If they make an 18% down payment, then they have already paid off 0.18×$170,000 = $31,500 for the home, leaving $143,500 that they need to pay over 15 years. They pay interest on that amount, though, at a rate of 2.75%, so they will not pay 100% of $143,500 over 15 years but rather 102.75% of $143,500, or 1.0275×143,500 = 147446.25 over 15 years. Dividing this payment up into 15×12 = 180 months, the monthly payment will be $147446.25/180 = $1,843 a month.