Question

In: Accounting

After graduating you have 55,000 in student debt with an interest rate of 9% compounded annually....

After graduating you have 55,000 in student debt with an interest rate of 9% compounded annually. Assume an annual payment over the next 10 years to make the problem simpler. After making 2 years of payments, you attend a social event hosted by SOFI and are considering refinancing your debt. The new refinanced interest rate would be 4.5% over a new 10-year term. You are in the 25% tax bracket. How much are you saving after taxes in year 3 of the original term if you refinance? Assume, again for simplicity, that all your Student loan interest paid is an itemized deduction on your personal income tax return. Round to the nearest dollar for all your calculations.

Expert Solution

Finding the monthly payment ,using the PV of annuity formula,

55000=Pmt.*(1-1.09^-10)/0.09

8570

Original loan amortisation table
Year	Annuity	Tow.Int.	Tow.Princ.	Princ.Bal
0				55000
1	8570	4950	3620	51380
2	8570	4624	3946	47434
3	8570	4269	4301	43133
4	8570	3882	4688	38445
5	8570	3460	5110	33335
6	8570	3000	5570	27766
7	8570	2499	6071	21694
8	8570	1952	6618	15077
9	8570	1357	7213	7864
10	8570	708	7862	2
Total	85700	30702	54998

Now, if refinanced at the start of Year 3, with the principal balance as 47434

47434=Pmt.*(1-1.045^-10)/0.045

5995

Revised payment schedule under refinancing will be
Year	Annuity	Tow.Int.	Tow.Princ.	Princ.Bal
0				47434
1	5995	2135	3860	43574
2	5995	1961	4034	39539
3	5995	1779	4216	35324
4	5995	1590	4405	30918
5	5995	1391	4604	26314
6	5995	1184	4811	21504
7	5995	968	5027	16476
8	5995	741	5254	11223
9	5995	505	5490	5733
10	5995	258	5737	-4
Total	59950	12512	47438

Before refinancing

Taxable interest after Itemized deduction of 2500

4269-2500=

1769

After refinancing

Taxable interest after Itemized deduction of 2500

0

(as the interest itself is 2135 only

so, after -tax savings of interest expenses=

(1769-0)*(1-25%)=

1326.75 or

1327

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