Answer:
Reinaldo will need to repay a total of approximately $566,261.91 to the bank over the 30-year term.
Explanation:
Reinaldo paid down 3% of the cost of the house, which is:
0.03 x $225,000 = $6,750
So he financed the remaining cost of the house, which is:
$225,000 - $6,750 = $218,250
To calculate the total amount he will need to repay the bank, we can use the formula for the monthly payment on a mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
where:
M is the monthly payment
P is the principal (the amount borrowed)
i is the monthly interest rate, which is the annual percentage rate (APR) divided by 12
n is the total number of monthly payments
First, we need to convert the APR of 7 1/2% to a monthly interest rate:
i = 7.5% / 12 = 0.00625
Next, we need to calculate the total number of monthly payments:
n = 30 years x 12 months/year = 360 months
Now we can plug in the values and calculate the monthly payment:
M = $218,250 [ 0.00625(1 + 0.00625)^360 ] / [ (1 + 0.00625)^360 – 1 ]
M ≈ $1,576.28
Finally, we can find the total amount he will need to repay the bank over the 30-year term by multiplying the monthly payment by the total number of payments:
Total amount = M x n
Total amount ≈ $1,576.28 x 360
Total amount ≈ $566,261.91
Therefore, Reinaldo will need to repay a total of approximately $566,261.91 to the bank over the 30-year term.