# Math Help - Unearned Interest Actuarial and Rule of 78

1. ## Unearned Interest Actuarial and Rule of 78

I keep getting the answer $107.79 for the Actuarial method. In the book it says$41.29 for actuarial and $39.70 for the rule of 78 method. Could someone please explain what I am doing wrong? The problem states each loan was paid off early and to find the unearned interest.Here is the problem. Amount financed is$3310, regular monthly payments are 201.85, with 18 payments scheduled. There are 6 remaining payments scheduled after payoff. I think the last part is what is tripping me.

2. Total Paid: $3,633.30 Total Interest Paid:$323.30

Rule of 78's

This is kind of a misnomer, since there are 18 payments. 1+2+3+...+18 = 171

Thus, the magic number is $323.30 / 171 =$1.89

Does that get you anywhere? You weren't dividing by 78, were you?

"Unearned Interest" is that interest that would have been paid, had the loan lived to original maturity. This is trivial for the Rule of 78's...

$1.89*(1+2+3+4+5+6) =$1.89(21) = 39.69 -- Okay, a little rounding problem.

It's a little trickier for the Actuarial. Let's see what you get.