Answer:
Range is always greater than zero.
Step-by-step explanation:
An exponential growth means that the growth rate of a given quantity increases exponentially.
The graph of an exponential function is shown below.
From the above graph, it's quite clear that the range of the function is never negative.
Hence, one characteristic of exponential growth is that the range(y values on the graph) is always greater than zero.
Answer:
The mortgage chosen is option A;
15-year mortgage term with a 3% interest rate because it has the lowest total amount paid over the loan term of $270,470
Step-by-step explanation:
The details of the home purchase are;
The price of the home = $275,000
The mode of purchase of the home = Mortgage
The percentage of the loan amount payed as down payment = 20%
The amount used as down payment for the loan = $55,000
The principal of the mortgage borrowed, P = The price of the house - The down payment
∴ P = $275,000 - 20/100 × $275,000 = $275,000 - $55,000 = $220,000
The principal of the mortgage, P = $220,000
The formula for the total amount paid which is the cost of the loan is given as follows;
The formula for monthly payment on a mortgage, 'M', is given as follows;
A. When the mortgage term, t = 15-years,
The interest rate, r = 3%
The number of months over which the loan is payed, n = 12·t
∴ n = 12 months/year × 15 years = 180 months
n = 180 months
The monthly payment, 'M', is given as follows;
M =
The total amount paid over the loan term = Cost of the mortgage
Therefore, we have;
220,000*0.05/12*((1 + 0.05/12)^360/( (1 + 0.05/12)^(360) - 1)
The minimum monthly payment for the loan, M ≈ $1,519.28
The total amount paid over loan term, A = n × M
∴ A ≈ 180 × $1,519.28 = $273,470
The total amount paid over loan term, A ≈ $270,470
B. When t = 20 year and r = 6%, we have;
n = 12 × 20 = 240
The total amount paid over loan term, A = 240 × $1,576.15 ≈ $378.276
The monthly payment, M = $1,576.15
C. When t = 30 year and r = 5%, we have;
n = 12 × 30 = 360
The total amount paid over loan term, A = 360 × $1,181.01 ≈ $425,163
The monthly payment, M ≈ $1,181.01
The mortgage to be chosen is the mortgage with the least total amount paid over the loan term so as to reduce the liability
Therefore;
The mortgage chosen is option A which is a 15-year mortgage term with a 3% interest rate;
The total amount paid over the loan term = $270,470