Loan payoff benefit versus raise. Break-even point needed

I have student loans that are under a program that pays off any remaining balance after 10 years of work. I become ineligible for this benefit if I change companies. So, I need to figure out, at what annual income, a raise would be a break even point for losing this loan payoff benefit, and taking another job.

The principal is 91,000 dollars. The Interest is 6 percent The time before the remaining balance will be payed off by the benefit program is 7 years. The monthly payment changes yearly based on my income. I have done some forecasting of my income to assume the average monthly payment over the next 7 years will be 700 dollars. This average payment, is not based on, but does correlate to an annual salary growth of approximately 6 percent per year. The annual salary is currently 56,000 dollars

Is there any additional information needed to perform the analysis?

• You say "the program pays off any remaining balance after 10 years" and that "the time before the remaining balance will be payed off by the benefit program is 7 years". So it appears you are three years into the program. Is the \$91,000 the 'current' balance of the loan? (which is being paid down from the current salary of \$56,000). If it is actually the initial principal of three years ago, then it would be better to state the current loan value and only consider the forthcoming seven year period. Otherwise we would need to know the details of the past payments. – Chris Degnen Jan 1 '17 at 22:03
• 91,000 dollars is the current remaining balance of the loan. I have been paying it down for three years under the benefit, so I have seven years remaining before the remaining balance (the balance remaining at that time) is payed off. Thank you for your comments. – MMc Jan 2 '17 at 0:17

It appears you are paying about 12.5% of your current salary of \$56,000 in order to average payments of \$700 per month over the next seven years, assuming an annual salary increase of 6%. E.g.

56000 / 12 * 0.125 = 583.33

Increasing by 6%

583.33  618.33  655.43  694.76  736.45  780.63  827.469

average over seven years = \$699.49

Here is a calculation of the present value of a loan, assuming constant annual salary increases of 6%. It is based on a more fully explained answer here: Unequal Loan Repayments.

This is how the repayments increase in the calculation. The present value calculation is based on this double summation: p = present value of loan
n = compounding periods per year = 12
r = nominal APR compounded monthly = 6 % = 0.06
i = monthly interest rate = r/n = 0.005
d = initial payment amount = \$583.33
y = number of years = 7
q = annual percentage increase in payments = 6 % = 0.06

By induction

p = (d (1 + i)^(-n y) ((1 + i)^n - 1) ((1 + i)^(n y) - (1 + q)^y))/
(i ((1 + i)^n - q - 1))

∴ p = \$47,219.40

So in seven years you will have paid down a portion of the current value of your debt worth \$47,219.40.

It appears \$91,000 was the initial loan value three years ago. However, if your current debt is \$91,000 you are set to pay \$47,219.40 of it, in today's value.

91000 - 47219.4 = 43780.6

\$43,780.60 would remain, which in 7 years would accumulate due to interest.

43780.6 (1 + i)^(n y) = 43780.6 (1 + 0.005)^84 = \$66,562.70

So in seven years the benefit program would be taking a debt of \$66,562.70 off your hands.

If you got another job today you would have to be \$66,562.70 better off in seven years to break even. Or if was the same salary but they gave you a golden hello of \$43,780.60 which you put towards your debt you would also break even.

Of course, if your current debt is not \$91,000 but lower, put in the actual balance to find the break-even value.

• 91,000 dollars is the current principal remaining. Thank you very much, this is a thorough analysis. This is exactly what I wanted to know. – MMc Jan 2 '17 at 0:21

protected by Community♦Mar 2 '18 at 23:41

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