Question

A couple who borrow $80,000 for 30 years at 8.4%, compounded monthly, must make monthly payments of $609.47. (a) Find their unpaid balance after 1 year. (Round your answers to the nearest cent.) (b) During that first year, how much do they pay towards the principle? (Round your answer to the nearest cent.) During that first year, what are their total payments? (Round your answer to the nearest cent.) $ During that first year, how much interest do they pay? (Round your answer to the nearest cent.) $

Answer 1

To answer this question, we need to develop an amortizing schedule:

Month	Opening Balance	PMT	Interest	Principal repayment	Closing Balance
1	$            80,000.00	$     609.47	$     560.00	$                            49.47	$          79,950.53
2	$            79,950.53	$     609.47	$     559.65	$                            49.82	$          79,900.71
3	$            79,900.71	$     609.47	$     559.30	$                            50.17	$          79,850.55
4	$            79,850.55	$     609.47	$     558.95	$                            50.52	$          79,800.03
5	$            79,800.03	$     609.47	$     558.60	$                            50.87	$          79,749.16
6	$            79,749.16	$     609.47	$     558.24	$                            51.23	$          79,697.94
7	$            79,697.94	$     609.47	$     557.89	$                            51.58	$          79,646.35
8	$            79,646.35	$     609.47	$     557.52	$                            51.95	$          79,594.41
9	$            79,594.41	$     609.47	$     557.16	$                            52.31	$          79,542.10
10	$            79,542.10	$     609.47	$     556.79	$                            52.68	$          79,489.42
11	$            79,489.42	$     609.47	$     556.43	$                            53.04	$          79,436.38
12	$            79,436.38	$     609.47	$     556.05	$                            53.42	$          79,382.96
		$ 7,313.64	$ 6,696.60	$                          617.04	$       956,040.54

Opening balance = previous year's closing balance
Closing balance = Opening balance-Principal repayment
PMT is calculated as per the above formula
Interest = 0.084 /12 x opening balance
Principal repayment = PMT - Interest

a) Unpaid or the closing balance after 1 year is  $956,040.54
b) Total principle repayment amount  for year 1 $617.04
c)Total payment for year 1   $7,313.64
d) Total interest payment for year 1  $6,696.60

Complete amortization schedule: