3. You decide to borrow $200,000 to build a new house. The bank charges an interest rate of 6% compounded monthly. If you pay the loan back over 30 years, what will your monthly payment be [rounded to the nearest dollar]?

200000 = pay[1 - 1.005^-360]/.005

1000 = paym[.833958072]
paym = 1000/.833958072
= $1199.10 or
$1199 to the nearest dollar

To calculate the monthly payment for a loan, you can use the formula for the monthly payment of a mortgage:

M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate divided by 12 and expressed as a decimal)
n = Number of monthly payments (loan term in years multiplied by 12)

In this case, the principal amount (P) is $200,000, the annual interest rate (r) is 6%, and the loan term (n) is 30 years.

First, we need to convert the annual interest rate to a decimal and find the monthly interest rate.

Monthly Interest Rate (r) = Annual Interest Rate / 12 = 6% / 12 = 0.06 / 12 = 0.005

Number of Monthly Payments (n) = Loan Term in Years * 12 = 30 * 12 = 360

Next, we can plug these values into the formula and calculate the monthly payment:

M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
M = (200,000 * 0.005 * (1 + 0.005)^360) / ((1 + 0.005)^360 - 1)

Using a calculator or spreadsheet, you can calculate M to find the monthly payment. Rounded to the nearest dollar, the monthly payment should be $1,199.