Question

Amy bought her house on Dec. 1 and took a $200,000 mortgage as part of the payment. The 15-year mortgage has a 7.2 percent nominal annual rate, but it calls for monthly payments beginning Jan. 1 next year. How much is the total interest paid after the 6th payment?

Answer 1

Particulars	Amount
Loan Amount	$           200,000.00
Int rate per month	0.6000%
No. of months	180

Monthly payment = Loan Amount / PVAF (r%, n)
Where
r is Int rate per Month = 7.2 % / 12 = 0.6 % or 0.006
n is No. of periods = 15 years * 12 = 180 months
= $ 200000 / PVAF (0.006 , 180)
= $ 200000 / 109.8845
= $ 1820.09
PVAF = [ 1 - [(1+r)^-n]] /r
= [ 1 - [(1+0.006)^-180]] /0.006
= [ 1 - [(1.006)^-180]] /0.006
= [ 1 - [0.34069]] /0.006
= [0.65931]] /0.006
= 109.8845

Period	Opening Bal	EMI	Interest	Principal Repay	Closing Outstanding
1	200000.00	1820.09	1200.00	620.09	199379.91
2	199379.91	1820.09	1196.28	623.81	198756.09
3	198756.09	1820.09	1192.54	627.56	198128.54
4	198128.54	1820.09	1188.77	631.32	197497.21
5	197497.21	1820.09	1184.98	635.11	196862.10
6	196862.10	1820.09	1181.17	638.92	196223.18
Total interest paid after the 6th payment			7143.743

Total interest paid after the 6th payment = $ 7142.743

Please comment if any further assistance is required