College Loan Repayment Calculations ?
This is a question for my Finance course and I keep getting stuck. Assume a student graduates and has $80,000 in student loans. There are 2 repayment options:
1. 10-year repayment, $1000 monthly payment
2. 20-year repayment, $700 monthly payment
Which of the above offers the lowest implied interest rate?
I think the point is to solve for the interest variable in both cases using this formula (see case 1 below) :
PV * (1 + i/12) ^ n = [PMT (1 + i/12) ^ n - (1)] / i/12
$80,000 * (1 + i/12) ^ 120 = [$1,000 (1 + i/12) ^ 120 – (1)] /
i/12
PV= Present Value
PMT = Monthly Payment
i/12 = Interest (per month)
n = 12 months * 20 years = 120 months
Does this sound correct or am I completely missing something? I tried to solve for i, but I can’t seem to get a solution. Can somebody please help me with this first case and walk me through the calcs? I need to make sure I’m on the right track! Any help would be greatly appreciated! Thank you!!!
You’re on the right track, but you’ve got to tweak a few things.
1) You have to think in compound rates, not nominal rates. Thus, let’s say the discount rate (i) is 12%. It’s not 12%/12 = 1% per month. Monthly interest is (1+i)^(1/PeriodsPerYear) 1.12^(1/12) = 0.9489% per month.
So you want to compare the PV of 1. which is 120 ‘n’ period with payments of 1000 at (i). Solve for PV.
vs.
PV of 2, which is 240 ‘n’ periods with payments of $700 at ‘i’, solve for PV.
Let’s say that i = 12%. Then ‘i per n’ is 0.9489%
1. PV = 71,454.8
2. PV = 66,122.5
PV of 2 is lower, so you want to take it because it costs you less money.
