Question

A 18 year loan is being repaid with level payments at the end of each month. The loan rate of interest is 15.6% compounded monthly. In which month is the interest portion approximately equal to 5 times principal the portion? Give an integer answer.

Answer 1

Let us assume $ 100000 as loan

EMI:

EMI = Loan / PVAF (r%, n)
PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

= $ 100000 / PVAF(1.3%, 216 )

= $ 100000 / 72.1979

= $ 1385.08

Loan Amortization:

As the full table is not supported by server, I am able to display portion where Int/ Principal is 5.

Month	Opening Bal	Instalment	Int	Principal Repay	Clsoing Bal	Int/ Principal
75	$ 89,523.51	$ 1,385.08	$ 1,163.81	$ 221.28	$ 89,302.23	5.26
76	$ 89,302.23	$ 1,385.08	$ 1,160.93	$ 224.15	$ 89,078.08	5.18
77	$ 89,078.08	$ 1,385.08	$ 1,158.02	$ 227.07	$ 88,851.01	5.10
78	$ 88,851.01	$ 1,385.08	$ 1,155.06	$ 230.02	$ 88,621.00	5.02
79	$ 88,621.00	$ 1,385.08	$ 1,152.07	$ 233.01	$ 88,387.99	4.94
80	$ 88,387.99	$ 1,385.08	$ 1,149.04	$ 236.04	$ 88,151.95	4.87
81	$ 88,151.95	$ 1,385.08	$ 1,145.98	$ 239.11	$ 87,912.84	4.79
82	$ 87,912.84	$ 1,385.08	$ 1,142.87	$ 242.21	$ 87,670.63	4.72
83	$ 87,670.63	$ 1,385.08	$ 1,139.72	$ 245.36	$ 87,425.27	4.65
84	$ 87,425.27	$ 1,385.08	$ 1,136.53	$ 248.55	$ 87,176.71	4.57
85	$ 87,176.71	$ 1,385.08	$ 1,133.30	$ 251.78	$ 86,924.93	4.50
86	$ 86,924.93	$ 1,385.08	$ 1,130.02	$ 255.06	$ 86,669.87	4.43
87	$ 86,669.87	$ 1,385.08	$ 1,126.71	$ 258.37	$ 86,411.50	4.36

Pls do rate, if the answer is correct and comment, if any further assistance is required.