Question

1. You are buying a new home with a purchase price of $189,500. You have a cash down payment of $18,950 and are financing the remaining amount at an interest rate of 4.5% for 30 years. Provide the following

1. 1. Principal amount to be repaid?
2. 2. Payment amount per month for 30 years   
3. 3. Total interest paid over 30 years?

2. Now suppose that you have financed the new house in problem #1 for 30 years. After 10 years into the Mortgage (April 2030), you’ve decided to make extra payments to pay the house off in 10 years (for a total of 20 years)

1. Current balance (April 2030)?
2. Total principal amount to be repaid?
3. New monthly payment amount?
4. Total interest amount paid over the 20 years?

Answer 1

1

a

Principal = 189,500 - 18,950 = 170,550

b

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          170,550
Rate of interest per period:
Annual rate of interest		4.500%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.045 /12 =	0.3750%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 170550 × 0.00375 × (1+0.00375)^360] / [(1+0.00375 ^360 -1]
Monthly payment	=	$                                                            864.15

Monthly payment is $864.15

c

Total interest pay:
Total payments	=	864.15 × 360
		$                                                    311,094.00
Less principle amount		$                                                    170,550.00
Interest payment- Finance charge		$                                                    140,544.00

Total interest is $140,544

2

a

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	170,550.00
Rate of interest	r=	0.3750%
nth payment	n=	120
Payment	P=	864.15
Loan balance	=	170550*(1+0.00375)^120 - 864.15*[(1+0.00375)^120-1]/0.00375
Loan balance	=	136,592.80

Current balance is $136,592.80

b

Principal is $136,592.80

c

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          136,593
Rate of interest per period:
Annual rate of interest		4.500%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.045 /12 =	0.3750%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	10
Total number of payments	N	10 × 12 =	120
Period payment using the formula	=	[ 136592.8 × 0.00375 × (1+0.00375)^120] / [(1+0.00375 ^120 -1]
Monthly payment	=	$                                                         1,415.63

New payment is $1,415.63

d

Interest for last ten years:

Total interest pay:
Total payments	=	1415.63 × 120
		$                                                    169,875.60
Less principle amount		$                                                    136,592.80
Interest payment- Finance charge		$                                                      33,282.80

Interest for first ten years =864.15*120-(170550-136592.8)		$                                                      69,740.80
Total interest		$                                                    103,023.60

Total interest paid is 103,023.60

please rate.