After graduating you have 55,000 in student debt with an interest rate of 9% com
ID: 2527314 • Letter: A
Question
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.
Explanation / Answer
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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