f ( P , r , N ), where P is the principal (the initial size of the loan), r the
ID: 2888262 • Letter: F
Question
f(P, r, N),
where P is the principal (the initial size of the loan), r the interest rate expressed as a decimal (a 6% interest rate is denoted by r = 0.06), and N the length of the loan in months.
11. + 2 points RogaCalcET3 14.4.037 My NotesAsk Your Teacher The monthly payment for a home loan is given by a function f(P, r, N), where p is the principal (the initial size of the loan), r the interest rate expressed as a decimal (a 696 | interest rate is denoted by r = 0.06), and N the length of the loan in months. If P = $100,000, r-0.06, and N-240 (a 20-year loan), then the m onthly payment is f(100,000, 0.06, 240)- 716.43. Furthermore, with these values, we have 5769, -1.5467. of = 5,769, ,of = aN -= 0.0072, Estimate the following values. (a) The change in monthly payment per $1,000 increase in loan principal. (b) The change in monthly payment if the interest rate increases to r = 6.5%. (c) The change in monthly payment if the length of the loan increases to 24 years. eBookExplanation / Answer
(a)
p =1000
f =(f/p)p
f =0.0072*1000
f =$ 7.2
(b)
r =(6.5%)-(6%)=0.065-0.06=0.005
f =(f/r)r
f =5769*0.005
f =$ 28.845
(c)
24 years =>N=24*12 = 288
N =288-240 =48
f =(f/N)N
f =-1.5467*48
f = - $ 74.2416
negative sign indicates monthly payment is decreased
absolute value will be f = $ 74.2416
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