Question

Your friend has just purchased a house and has incurred a $150,000, 4.5% mortgage payable at $760.03 per month. After making the first monthly payment, he receives a statement from the bank indicating only $197.53 had been applied to reducing the principal amount of the loan. Your friend then calculates that at the rate of $197.53 per month, it will take 63 years to pay off the $150,000 mortgage. Discuss and explain whether your friend’s analysis is correct or not.

Will  extra payments( payments above the $760.00 required payment) help your friend to pay off the mortgage more quickly and if so why or why not?

Answer 1

Interest for the first month = 150,000 * 4.5% * 1/12 = 562.50

Since of the total payment is applied first toward interest for the period, only 197.53 applied towards principal. But after applying 197.53 towrads principal amount, loan balance reduces to 149,802.57. Then interest is calculated on that balance.

It will not take 63 years but takes only 30 years to repay the loan. Because interest is calculated on reduced loan balance but not on original loan amount. Below amortization schedule shows how monthly payment reduces the loan balance.

Period	Opening liability	Total payment	Interest payment	Loan repaid	Closing liability
N	A	C	B= A* 0.003750	D=C-B	E=A-D
1	150,000.00	760.03	562.50	197.53	149,802.47
2	149,802.47	760.03	561.76	198.27	149,604.20
3	149,604.20	760.03	561.02	199.01	149,405.19
4	149,405.19	760.03	560.27	199.76	149,205.43
5	149,205.43	760.03	559.52	200.51	149,004.93
6	149,004.93	760.03	558.77	201.26	148,803.67
7	148,803.67	760.03	558.01	202.01	148,601.65
8	148,601.65	760.03	557.26	202.77	148,398.88
9	148,398.88	760.03	556.50	203.53	148,195.35
10	148,195.35	760.03	555.73	204.30	147,991.05

Any extra payment over and above required monthly payment reduces loan balance and pays off the loan amount even before 30 years.

At 30 years tenure only monthly payment comes to 760.03

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	150,000.00
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 =
Rate of interest per period	R	0.045 /12 =
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 =
Period payment using the formula	=	[ 150000*0.00375*(1+0.00375)^360] / [(1+0.00375 ^360 -1]
Monthly payment	=	760.03