Answer:
a) How long will it take to repay the loan?
20 years
b) What amount of interest does the purchase pay?
$134,896
Explanation:
a) How long will it take to repay the loan?
In the above question, they are asking you for the Loan duration
The Formula for Loan duration(T) =
ln (- m/(r÷n) × C - m)/In (1 + r/n)
Where:
m = monthly payments = $1395.40
C = Amount of mortgage =$200,000
r = Interest rate = 5.7% = 0.57
n = compounded quarterly = 4
T = ln (- 1395.40/(0.57÷4) × 200,000 - 1395.40)/In (1 + 0.57/4)
T = 20 years.
Therefore, it will take 20 years to repay the Loan.
b) What amount of interest does the purchase pay?
The total number of payments =
Loan duration × Number of months
Number of months = 12 months( because it is monthly payment)
Loan duration = 20 years
Total number of payments = 240 payments.
In the question, we are given the amount paid monthly payment as
$1,395.40
Total amount paid = Monthly payments × Total number of payments
= $1,395.40 × 240
= $334,896
The amount of Interest the purchase pay = $334,896 - $200,000
= $134,896