Answer:
the monthly payment for the mortgage is $2,460.62.
Explanation:
(a) To find the required down payment, we can use the fact that the bank requires a 10 1/6 (or 121/6) percent down payment on the $490,000 vacation home:
Down payment = (121/6)% of $490,000
= (121/6/100) * $490,000
= $80,166.67
Therefore, the required down payment is $80,166.67.
(b) To find the amount of the mortgage, we can subtract the down payment from the total cost of the vacation home:
Amount of mortgage = Total cost - Down payment
= $490,000 - $80,166.67
= $409,833.33
Therefore, the amount of the mortgage is $409,833.33.
(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment of a fixed-rate mortgage:
M = P * r * (1 + r)^n / [(1 + r)^n - 1]
where M is the monthly payment, P is the principal (or amount of the mortgage), r is the monthly interest rate (which is the annual interest rate divided by 12), and n is the total number of payments (which is the number of years times 12).
In this case, we have P = $409,833.33, r = 6%/12 = 0.005, and n = 30 * 12 = 360. Substituting these values into the formula, we get:
M = $409,833.33 * 0.005 * (1 + 0.005)^360 / [(1 + 0.005)^360 - 1]
= $2,460.62
Therefore, the monthly payment for the mortgage is $2,460.62.