You can afford a $1200 per month mortgage payment. You've found a 30 year loan at 7.3% interest.
a) How big of a loan can you afford? (Round to the nearest cent, as needed.)
$
b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)
$
c) How much of that money is interest? (Round to the nearest cent, as needed.)
$
I need Help
Assuming the rate is per annum, compounded monthly
i = .073/12 = .006083333..
n = 12(30) = 360
paym = 1200
PV = ?
PV = 1200(1 - 1.00608333...^-360)/.0060833...
=
Once you have that, compare it with
1200(360), the difference would be the interest.
Sure! Let's break down the problem step by step to find the answers.
a) To determine the size of the loan you can afford, we need to calculate the maximum monthly payment you can make. In this scenario, it is $1200.
We can use the formula for calculating the monthly payment on a mortgage loan:
Monthly Payment = Loan Amount * (r * (1+r)^n) / ((1+r)^n - 1)
Where:
- Loan amount is the principal
- r is the monthly interest rate
- n is the total number of monthly payments
To calculate the monthly interest rate (r), we divide the annual interest rate (7.3%) by 12 months: 0.073 / 12 = 0.0060833.
Next, we need to calculate the total number of monthly payments (n) for a 30-year loan. There are 12 months in a year, so n = 30 * 12 = 360.
Now, we can rearrange the formula to solve for the loan amount:
Loan Amount = Monthly Payment * ((1+r)^n - 1) / (r * (1+r)^n)
Plugging in the values:
Loan Amount = $1200 * ((1 + 0.0060833)^360 - 1) / (0.0060833 * (1 + 0.0060833)^360)
Using a calculator, the approximate loan amount you can afford is $180,842.23.
b) To calculate the total money paid to the loan company, multiply the monthly payment by the total number of payments:
Total Money Paid = Monthly Payment * Total Number of Payments
Total Money Paid = $1200 * 360
Using a calculator, the total amount paid to the loan company is $432,000.
c) To determine the amount of interest paid, subtract the loan amount (principal) from the total money paid:
Total Interest = Total Money Paid - Loan Amount
Total Interest = $432,000 - $180,842.23
Using a calculator, the total amount of interest paid is approximately $251,157.77.
Therefore, the answers are:
a) You can afford a loan amount of approximately $180,842.23.
b) You will pay a total of $432,000 to the loan company.
c) The amount of interest paid will be approximately $251,157.77.