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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Homework Help Forum: Business Math
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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.
To calculate the total finance charge on the loan, you need to understand how the Rule of 78 works. The Rule of 78 is a method of allocating interest charges over the duration of a loan. It assumes that the interest is precomputed and front-loaded, meaning a larger portion of the interest is charged earlier in the loan term.
To calculate the total finance charge, you can follow these steps:
1. Calculate the sum of the digits from 1 to 12 (since it is an 18-month loan). The sum of digits from 1 to 12 is 78 (1+2+3+...+12 = 78).
2. Determine the percentage of the total finance charge allocated to each month. For the first month, the percentage would be 12/78 (12% divided by 78). This represents the portion of the total finance charge related to the first month.
3. Multiply the percentage calculated in step 2 by the total loan amount of $1,700 to get the finance charge for the first month. In this case, the finance charge for the first month is (12/78) * $1,700 = $260.26.
4. Repeat step 3 for each subsequent month. Since Terry decides to pay back the loan at the end of the first month, you only need to calculate the finance charge for the first month. The total finance charge on the loan is $260.26.
Now, let's move on to calculating the unearned finance charge and what is needed to repay the loan.
The unearned finance charge represents the portion of the finance charge that has not been earned at the time of repayment. Since Terry decides to repay the loan at the end of the first month, the unearned finance charge would be the finance charge for the remaining 17 months.
To calculate the unearned finance charge, you can follow these steps:
1. Subtract the finance charge for the first month, which we calculated earlier, from the total finance charge on the loan. In this case, it would be $306 - $260.26 = $45.74.
2. The amount needed to repay the loan would be the remaining loan principal plus the unearned finance charge. Since Terry decides to repay the loan at the end of the first month, the remaining loan principal would be $1,700 minus the monthly installment paid.
Overall, the total finance charge on the loan is $306, and the unearned finance charge is $45.74. To fully repay the loan, you would need to calculate the remaining principal and add the unearned finance charge to it.