1. ## interest problems

Hey, I need help answering some problems I have

James is buying a house on a 30 year conventional mortgage at 6.25% APR. He will put 3% down on the loan. If he wants to keep his monthly payments at or below $1,000, how much is the most expensive house James can buy? Thanks 2. Hello, mandy! James is buying a house on a 30-year conventional mortgage at 6.25% APR. He will put 3% down on the loan. If he wants to keep his monthly payments at or below$1,000,
how much is the most expensive house James can buy?

The amortization formula is: .$\displaystyle P \;=\;A\,\frac{(1+i)^n - 1}{i(1+i)^n}$

. . where: .$\displaystyle \begin{Bmatrix}P &=& \text{principal amount of the loan} \\ A &=& \text{periodic payment} \\ i &=& \text{periodic interest rate} \\ n &=&\text{number of periods} \end{Bmatrix}$

We have: .$\displaystyle A = 1000,\;i = \frac{0.0625}{12},\;n = 360$

Then: .$\displaystyle P \;=\;1000\,\frac{\left(1+\frac{0.0625}{12}\right)^ {360}-1}{\frac{0.0625}{12}\left(1 + \frac{0.0625}{12}\right)^{360}} \;\approx\; \$162,412.22$This is the maximum amount he can borrow, . . which is 97% of the price of the house. Therefore, he can buy a house up to: .$\displaystyle \frac{\$162,412.22}{0.97} \;\approx\;\$167,435.28\$