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]?
1999
I answered this
http://www.jiskha.com/display.cgi?id=1268615820
To calculate the monthly payment for a loan, we can use the formula for the monthly payment on a fixed-rate mortgage:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1),
where:
M = monthly payment,
P = principal (loan amount),
r = monthly interest rate, and
n = total number of payments.
Given:
P = $200,000,
r = 6% per year = 6/100 = 0.06/12 = 0.005 (monthly interest rate),
n = 30 years * 12 months/year = 360 months.
Substituting these values into the formula, we have:
M = 200,000 * (0.005 * (1 + 0.005)^360) / ((1 + 0.005)^360 - 1).
To simplify the calculations, let's break it down step by step:
Step 1: (1 + r)^n = (1.005)^360
Step 2: Compute the numerator: 0.005 * (1.005)^360
Step 3: Compute the denominator: (1.005)^360 - 1
Step 4: Divide the numerator by the denominator: (0.005 * (1.005)^360) / ((1.005)^360 - 1)
Step 5: Multiply the principal by the result: 200,000 * ((0.005 * (1.005)^360) / ((1.005)^360 - 1))
Plugging these values into a calculator, we find that the monthly payment is approximately $1,199 (rounded to the nearest dollar).
Hence, your monthly payment for the loan will be around $1,199.