Answer:
Monthly amortization paid is $1,135
Amount of interest paid is $308,469
Step-by-step explanation:
Here, we are interested in calculating the monthly payment paid and the total value of this interest.
Firstly, we calculate the amount which this loan would be at the end of the 30 years.
To calculate this amount, we make use of the compound interest amount formula
A = P(1 + r/n)^nt
where A is the amount we want to calculate
P is the amount borrowed which is $100,000
r is the interest rate which is 4.7% or simply 4.7/100 = 0.047
n is the number of times yearly which the interest is compounded which is 12 since it is compounded monthly
t is the total time taken to repay the loan which is 30 years
Plugging these values, we have
A = 100,000( 1 + 0.047/12)^(12 * 30)
A = 100,000( 1+ 0.00392)^360
A = 100,000(1 .00392)^360
A = $408,469
The monthly payment needed to amortize the loan will be the amount after 30 years divided by the number of months in 30 years
The number of months in 30 years is 30 * 12 = 360 months
The monthly payment amount is thus 408,469/360 = 1,134.6 approximately $1,135
The total interest paid will be the amount minus the principal
This is $408,469 - $100,000 = $308,469
