Question

The Centurion Corp. is putting together a financial plan for the company covering the next three years, and it needs to forecast its interest expense and the related tax savings. The firm’s most significant liability is a fully amortized mortgage loan on its real estate. The loan was made exactly ten and one-half years ago for $3.2M at 11% compounded monthly for a term of 30 years. Use the AMORTIZ program to predict the interest expense associated with the real estate mortgage over the next three years. (Hint: Run AMORTIZ from the loan’s beginning and add up the months in each of the next three years.)

Answer 1

Let us start by finding out the Principal balance at end of 10&1/2 years

For that, we need to know thw monthly payment towards the mortgage

which we shall find by using the PV of ordinary annuity formula,

PVOA=Pmt.(1-(1+r)^-n)/r

where

PVOA= the loan amt.= $ 3200000

Pmt.= the monthly pmt. To be found out---- ??

r= monthly interest rate= 11%/12=0.00917

n=no.of mthly. compounding periods=30 yrs. *12 mths.= 360

Putting the values in the formula,

we find the equal mthly. Pmt. As

3200000=Pmt.(1-1.00917^-360)/0.00917

30484

Now, we can find the Principal balance at end of 10&1/2 years ,ie.(10*12)+6= 126 mths.

Principal balance at end of 126 th mth. Is given by the formula,

FV=PV*(1+r)^n-(P*(((1+r)^n-1)/r))

where,

FV= Future value ,ie. The remaining principal balance

PV=Present value,ie. Original loan balance=3200000

P=Mthly pmt. =30484

r=rate /mth--0.00917

n=no.of pmts.=126

Putting the values in the above formula,

FV=(3200000*(1.00917)^126)-(30484*(((1+0.00917)^126-1)/0.00917))=

2931636.

With this principal balance, we can draw up the amortisation schedule of the mortgage for the next 3 yeare,ie. 3*12=36 months

No.	Mthly. Pmt. No.	Mthly.pmt.	Tow. Interest expense	Tow. Principal	Principal balance
0	126				2931636
1	127	30484	26883	3601	2928035
2	128	30484	26850	3634	2924401
3	129	30484	26817	3667	2920734
4	130	30484	26783	3701	2917033
5	131	30484	26749	3735	2913298
6	132	30484	26715	3769	2909529
7	133	30484	26680	3804	2905726
8	134	30484	26646	3838	2901887
9	135	30484	26610	3874	2898013
10	136	30484	26575	3909	2894104
11	137	30484	26539	3945	2890159
12	138	30484	26503	3981	2886178
13	139	30484	26466	4018	2882160
14	140	30484	26429	4055	2878106
15	141	30484	26392	4092	2874014
16	142	30484	26355	4129	2869884
17	143	30484	26317	4167	2865717
18	144	30484	26279	4205	2861512
19	145	30484	26240	4244	2857268
20	146	30484	26201	4283	2852985
21	147	30484	26162	4322	2848663
22	148	30484	26122	4362	2844301
23	149	30484	26082	4402	2839900
24	150	30484	26042	4442	2835457
25	151	30484	26001	4483	2830975
26	152	30484	25960	4524	2826451
27	153	30484	25919	4565	2821885
28	154	30484	25877	4607	2817278
29	155	30484	25834	4650	2812628
30	156	30484	25792	4692	2807936
31	157	30484	25749	4735	2803201
32	158	30484	25705	4779	2798422
33	159	30484	25662	4822	2793600
34	160	30484	25617	4867	2788733
35	161	30484	25573	4911	2783822
36	162	30484	25528	4956	2778865
Total		1097424	944653	152771

OR
can also be worked out as follows:
if, only the total interest expense for the 36 mths.is needed
Future value at the end of 162nd mth.
FV=(3200000*(1.00917)^162)-(30484*(((1+0.00917)^162-1)/0.00917))=
2778865.557
FV at end of 10& 1/2 yr. or 126 mths.(calculated as above-in the beg.)	2931636
Principal loan amt.	3200000
So,total amt. paid towards principal   in these 126 months	268364
Total amt. of mthly.annuities in 126 mths.(30484*126)	3840984
So, amt. towards int.for 126 mths	3572620
FV at end of 162 mths.	2778866
Principal loan amt.	3200000
So,total amt. paid towards principal   in these 162 months	421134
Total amt. of mthly.annuities paid(30484*162)	4938408
So, amt. towards int.for 162 mths	4517274
So, interest expense for the next 36 mths.(4517274-3572620)	944654