Suppose that you want to purchase a home for $450,000 with a 30 year mortgage at 6% interest. Suppose that you can put 20% down. Assume that the monthly cost to finance $1,000 is $6.00. What are the monthly payments?
% Financed = 100% - 20% = 80%.
Amt. Financed=0.80 * 450,000 = $360000.
Monthly Payment=(360000/1000) * 6 = $2160.
To calculate the monthly payments on a mortgage, you need to consider the loan amount, interest rate, and the loan term.
First, let's calculate the down payment. Given that you can put 20% down on a $450,000 home, the down payment would be 20% of $450,000 which is $90,000.
Next, calculate the loan amount by subtracting the down payment from the purchase price: $450,000 - $90,000 = $360,000.
To calculate the monthly interest rate, divide the annual interest rate by 12. In this case, the annual interest rate is 6%, so the monthly interest rate is 6% / 12 = 0.5%.
To calculate the monthly mortgage payment amount, you can use the formula for a fixed-rate mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = monthly mortgage payment
P = loan amount
i = monthly interest rate
n = the number of monthly payments
Using the given values, we have:
P = $360,000,
i = 0.005, and
n = 30 years * 12 months/year = 360 months.
Now, plug these values into the formula and calculate the monthly mortgage payment:
M = $360,000 [(0.005(1 + 0.005)^360)] / [(1 + 0.005)^360 - 1]
Using a calculator or a spreadsheet, compute this expression to find the monthly mortgage payment:
M ≈ $2,147.29
Therefore, the monthly mortgage payment for a $450,000 home with a 30-year mortgage at 6% interest, with a 20% down payment, is approximately $2,147.29.