Question

4. A. What would be your mortgage payment if you pay for a $250,000 home by making a 20% down payment and then taking out a 3.74% thirty year fixed rate mortgage loan to cover the remaining balance. All work must be shown justifying the following answers?

                                                                                                            Mortgage payment = _______________

B. How much total interest would you have to pay over the entire life of the loan?

                                                                                                            Total interest paid = __________

C. Suppose you inherit some money and decide to use it to pay the loan off early by paying the unpaid balance of the loan after having made the regularly scheduled 240^th payment. Assuming there is no prepayment penalty charged, what payment will be required to pay this loan off at this time?

                                                                            Amount required to pay loan off early _____________

D) How much interest will you have saved by paying the loan off early after making the 240^th payment?

E. Suppose you decided to pay for this house by taking out a fifteen year 3.04% fixed rate mortgage instead of the thirty year 3.74% fixed rate mortgage.          What would be your required mortgage payment for this 15 year mortgage assuming you still make the same 20% down payment.

F. How much interest would you have saved by taking out the fifteen year fixed rate mortgage instead of the thirty year fixed rate mortgage?

                                                                                                            Interest saved = _______________

G. Taking the above data into account, write a short paragraph comparing what you feel are the pros and cons of each type of mortgage?

I need help with D through G !!!!

Answer 1

Q4A.

We will need use the Capital Recovery formula to calculate the Mortgage Payment, Interest. "The Capital Recovery factor is the ratio of a constant annuity to the present value of receiving that annuity for a given length of time".

The formula for Capital Recovery Factor (CRF) is: (i(1+i)^n) / ((1+i)^n-1).

We use the Capital Recovery Factor formula to determine the monthly Mortgage Payments and Interest on a fixed rate, 30 year mortgage.

The monthly Mortgage Payment "P" = A (Total Amount of Mortgage) * Capital Recovery Factor

Therefore, P = A* ((i*(1+i)^n) / ((1+i)^n-1))

i = Interest rate = 3.74% per year or 3.74/12 = 0.311666 or 3.116666%

n = No. of periods or 12 per year and 360 for 30 years.

Step 1	Determine the Total Amount of Mortgage
Given		Amount -$
1	Cost of home	250,000
2	Downpayment - %	20%
3	Total Amount of Mortgage = Cost * (1-Downpayment %) "A"	200,000
Step 2	Determine Capital Recovery Factor (CRF) for 30 years at 3.74% per year
Formula	Therefore, CRF = ((i*(1+i)^n) / ((1+i)^n-1))
Where,
i	Interest rate = 3.74% per year or 3.74/12 = 0.311666 or 3.116666%
n	No. of periods or 12 per year and 360 for 30 years
	CRF = (3.74%/12*(1+3.74%/12)^(30*12))/ ((1+3.74%/12)^(30*12)-1)
=>	CRF = (0.00311666*(1+0.00311667)^(360))/ ((1+0.0031166667)^(360)-1)
	Numerator of formula
=>	(1+3.74%/12) ^ 360 =	3.065636375
I	3.74%/12* 3.06563638 =	0.009554567
	Denominator of formula
=>	(1+3.74%/12)^360	3.065636375
II	(1+3.74%/12)^360 -1	2.065636375
	Capital Recovery Factor = I/II	0.004625483
Step 3	Determine monthly Mortgage Payment
P	Amount of Monthly Mortgage	200,000
CRF	Capital Recovery Factor	0.004625483
Q4(A)	The Total Payment "P" = A* CRF - Answer	$ 925.09667
Q(B) 4	Determine Total Interest Payments
Formula	Interest I = ( Monthly Payment * Total No. of months in 30 years)-Principal
=>	Interest (i) = ($ 925.09667*360)-200,000
=>	I = $333,034.8027-$200,000
Answer	Total Interest (i) =	$133,034.80

Q 4 (c )		Amount-$	Amount -$
A	Total amount of Mortgage Loan		200,000.00
Add
B	Interest at 3.74% p.a for 360 months as determined in Q 4 (b)		133,034.80
C	Total value of Loan + Interest for 360 months		333,034.80
Less
D	Amount of Principal & Interest that would be paid off after 240 months (925.09667*240)		222,023.20
E	Balance Amount to be paid ( Including Interest & Principal - $ 925.09667*120 months)		111,011.60
	Of which:
F1	Principal	92,496.66
F2	Interest at 3.74% p.a	18,514.94
Answer C	Amount to be paid off will be equal to the balance of principal remaining to be paid	92,496.66
Answer D	Interest saved by pre-paying= Interest balance	18,514.94

Q 4 E
Step 1	Determine the Total Amount of Mortgage
Given		Amount -$
1	Cost of home	250,000
2	Downpayment - %	20%
3	Total Amount of Mortgage = Cost * (1-Downpayment %)	200,000
Step 2	Determine Capital Recovery Factor (CRF) for 15 years at 3.04% per year
Formula	Therefore, CRF = ((i*(1+i)^n) / ((1+i)^n-1))
Where,
i	Interest rate = 3.04% per year or 3.04/12 = 0.00253333	0.002533333
n	No. of periods or 12 per year and 180 (15*12)months for 15 years
	CRF = (3.04%/12*(1+3.04%/12)^(15*12))/ ((1+3.04%/12)^(15*12)-1)
=>	CRF = (0.00253333*(1+0.00253333)^(360))/ ((1+0.0025333333)^(360)-1)
	Numerator
=>	(1+3.04%/12) ^ 180 =	1.576840835
I	3.04%/12* 1.576840835 =	0.003994663
	Denominator
=>	(1+3.04%/12)^180	1.576840835
II	(1+3.04%/12)^180 -1	0.576840835
	Capital Recovery Factor = I/II	0.006925071
Step 3	Determine monthly Mortgage Payment
P	Total Amount of Mortgage	$200,000
CRF	Capital Recovery Factor	0.006925071
Answer 4E	The Total Payment = P * CRF	$1,385.01
Step 4	Determine Total Interest Payments
Formula	Interest I = ( Monthly Payment * Total No. of months in 15 years)-Principal
=>	Interest (i) = ($ 1385.01*180)	249,302.54
=>	I = $249,302.54-$200,000
Answer	Total Interest (i) =	$49,302.54
Answer Q 4(F)
A.	Original Interest Payment for 360 months at 3.74% p.a	133,034.80
Less
B.	New Interest payment for 180 months at 3.04%	49,302.54
C.	Savings in interest ( A-B)	83,732.26

Q 4(G)

Pros and Cons of Each type of Mortgage

In any mortgage loan, the Principal component of the total payment will increase over the duration of the loan. However, the interest amount will reduce over the same period.

Therefore, paying off a mortgage earlier than the maturity period, will save very little interest. This could be seen in the answers to Q 4(C) & (D). The amount saved by paying off the balance due i.e., $ 92,496.66, from an inheritance due after the 240 month saved only $18,514 by way of interest.

The shorter the mortgage period and lower the mortgage interest, the higher will the the Mortgage payment (Principal & Interest). Further, if we opt for mortgage loan for a shorter perio, there will be a saving in interest, when compared to a mortgage for a longer period at higher rate of interest.