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Terry has an 18-month installment loan for \$1,700 at 12% annual interest. Interest is compunded using the Rule of 78. Terry decides to pay back the loan at the end of the first month.

1. What is the total finance charge on the loan?
The answer is \$306, but I don't see how you get that.
2. What is the unearned finance charge, and what is needed to repay the loan?
I don't know how to go about doing this at all.

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Posted by Tracy on Monday, January 14, 2008 at 5:23pm.

Terry has an 18-month installment loan for \$1,700 at 12% annual interest. Interest is compunded using the Rule of 78. Terry decides to pay back the loan at the end of the first month.

1. What is the total finance charge on the loan?
The answer is \$306, but I don't see how you get that.
2. What is the unearned finance charge, and what is needed to repay the loan?

Simple interest total:
Interest = rate x Time x Principal
.........= .01..x..18..x...1700 = \$306.

Sum of months = n(n + 1)/2 = 18(19)/2 = 171

Month 1 - I = 306(18/171) = \$32.21
Month 2 - I = 306(178/171) = \$30.42
Month 3 - I = 306(16/171) = \$28.63

Month 17 - I = 306(2/171) = \$3.58
Month 18 - I = 306(1/171) = \$1.79

Interest plot is essentially a straight line making the total interest equal to I = (32.21 + 1.79)/2 = 17(18) = \$306.

Total outlay to repay the loan = 1700 + 306 = \$2006.

The monthly payment for a conventionsl loan would be
R = 1700(.01)/[1 - (1.01)^-18] = \$103.67.
Total outlay = 133.67(18) = \$1866.05 for a total interest payment of \$166.06.

The rule of 78 loan approach cost \$139.95 more.