Loan payoff benefit versus raise. Break-even point needed

Question

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?

Answer 1

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.