Question

Johnson and Johnson purchased a house for $450000. The had a 35%
down payment and negotiated a four year mortgage at 4:35% amortized over 20
years.
(a) Calculate their monthly payments.
(b) After the four year term was completed, they renegotiated a new term for
six years at 2:15% amortized over 15 years. Determine their new monthly
payments.

Answer 1

We need the find the annual worth of the house at an interest rate of 4.35%.

\[A = P \left[ i(1+i)^n \over (1+i)^n -1 \right]\]where P is the present worth of the loan (price of house - down payment), i is the interest rate, and n is the number of compounding periods (20 in this case), and A is the annual payments. To get A in terms of monthly payments, divide the interest rate by 12, and multiply n by 12.

Answer 2

yes i believe i understood this 450000*35
450000-157500 = 292500 is the monthly payment?

and their new payment is 2329.4?

Answer 3

I got the monthly payment to be 1826.90 for part a.

Answer 4

hmm did you you do it the way i did it or is it cool if u show me how u did it

Answer 5

I used the above equation. For a 20 year mortgage, n = 12*20 = 240, i = 0.0435/12 = 0.003625, and P = 292500. The above equation becomes\[A = 292,500 \left[0.003625*(1.003625)^{240} \over (1.003625)^{240} -1 \right]\]

Answer 6

oh wow lol what about thier new payment is it 2329.4? or im i just wrong lhaha

Answer 7

We need the find the current value of the loan after 4 years.

Take 292500 and subtract 48*A from it. Then redo the formula with the new interest rate and n values.

Answer 8

wait i dont get it

Answer 9

After four years, we negotiate a new mortgage rate right? During those four years were were making payments. Therefore, the present value of the loan after those four years is equal to \[P_4 = P_1 - 4*12*A\] because we have made fours years worth of payments. P1 is 292500 and A is the monthly payment we calculated for part a.

You with me?

Answer 10

so p4= 292500-4*12*1826.90=204808.8

Answer 11

Indeed.

Answer 12

yes im with you

Answer 13

sweet! i have one more question

Answer 14

Now we need to determine the monthly payment required to pay off this new P value using the new mortgage data.

Answer 15

Ok. Ask away!

Answer 16

which? data

Answer 17

and my question is

(a) y = 4:75 sin(3x + 1) 􀀀 5
(b) y = 0:86 sin(0:5x) + 0:54
state the following:
(a) maximum value
(b) minimum value
(c) amplitude
(d) period
(e) median value
(f) start point

Answer 18

2.15% interest rate, 15 years worth of payments. Just like before when we had a 4.35 interest rate and 20 years worth of payments. You have new i and n values for part b.

Answer 19

equation a. is that sin - 5 or + 5?

Answer 20

- 5

Answer 21

Okay. What is the maximum y-value of y=sin(x) and y=cos(x)?

Answer 22

and boss i thought we finished calculating the firrst question b, could you please show me the steps i have to take for the first question..b

Answer 23

max= -0.25
min=-9.75amp=4.75 and i dont know how to solve for the rest

Answer 24

\[A = P_4 \left[ {(2.15/12)(1+2.15/12)^{12*15} \over (1+2.15/12)^{12*15} -1} \right]\]

Answer 25

whats the final answer come to

Answer 26

The period of sin(x) is 1/(2pi). So the period of sin(3x+1) is 3/(2pi). The start point of sin(x) is zero. The start point of sin(3x+1) is shifted one to the left on the x-axis. The median value is the average of the maximum and minimum amplitude.

Answer 27

The value of the second A is 1,332.16.

Answer 28

I'm sorry. The period of sin(x) is 2pi. The period of sin(3x+1) is (2pi)/3

Answer 29

for the period its 2.09 and sp=0 and m=?

Answer 30

I told you what they were. SP = -1 and Median is the average of the max and min amplitudes. You know how to calculate the average?

Answer 31

amp= 4.75 is this correct?

Answer 32

no i honestly dont know how to calculate the average

Answer 33

No. If we had sin(x), the function would go from +1 to -1 right? Therefore, the median value would be 0. In this cause, the maximum amplitude is -0.25 and the minimum amplitude is - 9.75. The median amplitude is \[M = {-0.25 - 9.75 \over 2} = -5\]

Answer 34

wow honestly ur the best! thank you sooo freakin much man!cant thank u enough lol i have a hard time figuring out this stuff and thanks for showing me them in steps (=

Answer 35

You're welcome. Take a look at this: http://www.wolframalpha.com/input/?i=4.75*sin%283x%2B1%29+-5 It will help you visualize the plot.

Answer 36

cool

Answer 37

wait last question im really sorry about that!
y = 0:86 sin(0:5x) + 0:54