Question: The price of a home is $180,000. The bank requires a 10% down payment. After the down payment, the balance is financed with a 30 year fixed mortgage at 6.3%. Determine the unpaid balance after ten years.

Question

Question: The price of a home is $180,000. The bank requires a 10% down payment. After the down payment, the balance is financed with a 30 year fixed mortgage at 6.3%. Determine the unpaid balance after ten years. 
Answer: The unpaid balance after ten years is $136,641.85

I have the answer but I need help figuring out the formula used and the steps taken to get the answer. Please help.

Reiny · Answer

First you have to find the payment.
You did not say, but I will assume that the payments are monthly.
let the payment be p

162000 = p( 1 - 1.00525^-360)/.00525
p = 1002.74

unpaid balance after 10 years
= balance if you had paid nothing - amount of the annuity for 10 years
= 162000(1.00525)^120 - 1002.74(1.00525^120 - 1)/.00525
= 136641.30

could be round-off error on their part, I kept max number of decimals using calculator's memories.