Explanation:
a. To find the loan amount, you'll need to calculate 90% of the home's price, as you're making a 10% down payment:
Loan amount = 90% of $200,000
Loan amount = 0.90 * $200,000
Loan amount = $180,000
So, the loan amount will be $180,000.
b. To calculate the monthly payments with a 30-year loan at a 5% interest rate, you can use the formula for a fixed-rate mortgage payment. The formula is:
M = P[r(1 + r)^n] / [(1 + r)^n - 1]
Where:
M = Monthly payment
P = Principal loan amount (which is $180,000)
r = Monthly interest rate (5% annual rate divided by 12 months, so 0.05 / 12)
n = Total number of payments (30 years, or 30 * 12 months)
Now, plug these values into the formula:
M = $180,000[0.0041667(1 + 0.0041667)^(3012)] / [(1 + 0.0041667)^(3012) - 1]
M ≈ $966.28
So, with a 5% interest rate, your monthly payments will be approximately $966.28.
c. To calculate the monthly payments with a 30-year loan at a 6% interest rate, you can use the same formula, just change the interest rate:
r = 6% annual rate divided by 12 months, so r = 0.06 / 12 = 0.005
Now, plug in the values and calculate:
M = $180,000[0.005(1 + 0.005)^(3012)] / [(1 + 0.005)^(3012) - 1]
M ≈ $1,079.27
So, with a 6% interest rate, your monthly payments will be approximately $1,079.27.
I hope this helps!