Question

A loan of $10,000 is amortized by equal annual payments for 30 years at an effective annual interest rate of 5%. The income tax rate level is at 25%. Assume the tax on the interest earned is based on the amortization schedule.

a) Determine the income tax in the 10th year

b) Determine the total income taxes over the life of the loan

c) Calculate the present value of the after-tax payments using the before-tax yield rate. Answer to the nearest dollar.

Answer 1

We are given the following data:

Principal (P) = $10,000
No. of years N = 30
Interest rate r = 5%
Tax rate t = 25%

To answer the questions, we first need to prepare the amortization schedule. The annual payment or installment (I) on the loan can be calculated by using the formula to find the present value of future cash flows.

Rearranging the above equation, we get

Substituting the values in the above formula, the installment I comes to $651. From this, we can the prepare the below amortization schedule. In addition to the columns forming part of the standard amoritzation schedule, the below schedule also includes the columns 'Income tax', 'Interest after tax' and 'Present value of interest after tax' for ease of reference. Please note that the amounts in the table are in $.

Year	Installment (A)	Interest (B)	Principal (A - B)	Loan Balance	Income tax (C = B*25%)	Interest after tax (B - C)	Present value of interest after tax
1	651	500	151	9,849	125	375	357
2	651	492	158	9,691	123	369	335
3	651	485	166	9,526	121	363	314
4	651	476	174	9,351	119	357	294
5	651	468	183	9,168	117	351	275
6	651	458	192	8,976	115	344	257
7	651	449	202	8,775	112	337	239
8	651	439	212	8,563	110	329	223
9	651	428	222	8,340	107	321	207
10	651	417	233	8,107	104	313	192
11	651	405	245	7,862	101	304	178
12	651	393	257	7,604	98	295	164
13	651	380	270	7,334	95	285	151
14	651	367	284	7,050	92	275	139
15	651	353	298	6,752	88	264	127
16	651	338	313	6,439	84	253	116
17	651	322	329	6,111	80	241	105
18	651	306	345	5,766	76	229	95
19	651	288	362	5,403	72	216	86
20	651	270	380	5,023	68	203	76
21	651	251	399	4,624	63	188	68
22	651	231	419	4,204	58	173	59
23	651	210	440	3,764	53	158	51
24	651	188	462	3,302	47	141	44
25	651	165	485	2,816	41	124	37
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