Question

A loan is to be repaid over 30 years, with month-end repayments of 3,000. If the interest rate is 6.5% p.a. compounded monthly. Calculate the principal paid for year 10. Correct your answer to the nearest cent without any units. (Do not use "$" or "," in your answer. e.g. 12345.67)  

Answer 1

EMI = Loan Amount / PVAF (r%, n)

PVAF = Sum [ PVF (r%, n) ]

PVF (r%, n) = 1 / ( 1 + r)^n

EMI = Loan Amount / PVAF (r%, n)

3000 = Loan AMount / PVAF(0.5417%,360)

Loan Amount = 3000 * PVAF ( 0.5417% , 360)

= $ 3000 * 158.2108

= $ 474,632.46

Loan Amortization Schedule:

Month	Opening Balance	EMI	Int	Principal Repay	Closing Balance
102	$      4,17,150.61	$ 3,000.00	$ 2,259.57	$    740.43	$ 4,16,410.17
103	$      4,16,410.17	$ 3,000.00	$ 2,255.56	$    744.44	$ 4,15,665.73
104	$      4,15,665.73	$ 3,000.00	$ 2,251.52	$    748.48	$ 4,14,917.25
105	$      4,14,917.25	$ 3,000.00	$ 2,247.47	$    752.53	$ 4,14,164.72
106	$      4,14,164.72	$ 3,000.00	$ 2,243.39	$    756.61	$ 4,13,408.11
107	$      4,13,408.11	$ 3,000.00	$ 2,239.29	$    760.71	$ 4,12,647.40
108	$      4,12,647.40	$ 3,000.00	$ 2,235.17	$    764.83	$ 4,11,882.58
109	$      4,11,882.58	$ 3,000.00	$ 2,231.03	$    768.97	$ 4,11,113.61
110	$      4,11,113.61	$ 3,000.00	$ 2,226.87	$    773.13	$ 4,10,340.47
111	$      4,10,340.47	$ 3,000.00	$ 2,222.68	$    777.32	$ 4,09,563.15
112	$      4,09,563.15	$ 3,000.00	$ 2,218.47	$    781.53	$ 4,08,781.62
113	$      4,08,781.62	$ 3,000.00	$ 2,214.23	$    785.77	$ 4,07,995.85
114	$      4,07,995.85	$ 3,000.00	$ 2,209.98	$    790.02	$ 4,07,205.83
115	$      4,07,205.83	$ 3,000.00	$ 2,205.70	$    794.30	$ 4,06,411.53
116	$      4,06,411.53	$ 3,000.00	$ 2,201.40	$    798.60	$ 4,05,612.92
117	$      4,05,612.92	$ 3,000.00	$ 2,197.07	$    802.93	$ 4,04,809.99
118	$      4,04,809.99	$ 3,000.00	$ 2,192.72	$    807.28	$ 4,04,002.71
119	$      4,04,002.71	$ 3,000.00	$ 2,188.35	$    811.65	$ 4,03,191.06
120	$      4,03,191.06	$ 3,000.00	$ 2,183.95	$    816.05	$ 4,02,375.01
121	$      4,02,375.01	$ 3,000.00	$ 2,179.53	$    820.47	$ 4,01,554.54
122	$      4,01,554.54	$ 3,000.00	$ 2,175.09	$    824.91	$ 4,00,729.63
123	$      4,00,729.63	$ 3,000.00	$ 2,170.62	$    829.38	$ 3,99,900.25
124	$      3,99,900.25	$ 3,000.00	$ 2,166.13	$    833.87	$ 3,99,066.38
125	$      3,99,066.38	$ 3,000.00	$ 2,161.61	$    838.39	$ 3,98,227.99
126	$      3,98,227.99	$ 3,000.00	$ 2,157.07	$    842.93	$ 3,97,385.05

Principal paid in Year 10 = Principal apportion from 109 to 120 Months

I.e $ 9507.56