A couple has just purchased a home for $311,500.00. They will pay 20% down in cash,...

A couple has just purchased a home for $311,500.00. They will pay 20% down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of 4.08% APR with monthly compounding. The mortgage has a term of 30 years.

What is the size of the loan taken out by the couple?

What is the monthly payment on the loan?

How much interest is paid on the first payment?

How much interest is paid in the first year?

Expert Solution

Payment:	#
Asset Value = A	$311,500.00
Down Payment = DP =	$62,300.00
P = Principal Loan = (A - DP) =	$249,200.00
R = Rate or APR =	4.08%
N = Number of payments =	360
PMT = Payment = P x R/12 x (1+R/12)^N / ((1+R/12)^N - 1)
Payment = Payment in Dollars = 320000 x 6%/12 x (1+6%/12)^360 / ((1+6%/12)^360 -1) =	$1,201.24

Alternate Method:
Using financial calculator BA II Plus - Input details:	#
I/Y = Rate/12*100 =	0.340000
FV =	$0
N = Total terms =	360
PV =	-$249,200
CPT > PMT = Monthly Payment =	$1,201.24

What is the size of the loan taken out by the couple? $249,200.00

---------------------------

What is the monthly payment on the loan? $1,201.24

---------------

How much interest is paid on the first payment?

Interest = Loan value x Rate/12 = 249200 x 4.08%/12 = $847.28

---------------------------------

How much interest is paid in the first year? $ 10,087.02 (sum of interest column)

Year	Opening balance of loan	Interest	Payment	Amortization of loan	Closing balance
Y	OP	I = OP x Rate	PMT	AM = PMT - I	CB
1	249,200.00	847.28	$1,201.24	353.96	248,846.04
2	248,846.04	846.08	$1,201.24	355.16	248,490.87
3	248,490.87	844.87	$1,201.24	356.37	248,134.50
4	248,134.50	843.66	$1,201.24	357.58	247,776.92
5	247,776.92	842.44	$1,201.24	358.80	247,418.12
6	247,418.12	841.22	$1,201.24	360.02	247,058.10
7	247,058.10	840.00	$1,201.24	361.24	246,696.86
8	246,696.86	838.77	$1,201.24	362.47	246,334.39
9	246,334.39	837.54	$1,201.24	363.70	245,970.68
10	245,970.68	836.30	$1,201.24	364.94	245,605.74
11	245,605.74	835.06	$1,201.24	366.18	245,239.56
12	245,239.56	833.81	$1,201.24	367.43	244,872.13
	Total Interest	10,087.02

jeff jeffy answered 2 years ago

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