A $400 loan is to be paid off in 66 monthly payments of $11.62. The borrower decides to pay off the loan after 18 payments. Use the rule of 78s to find the amount of interest saved. (Points : 1)
$194.13
I get a slightly different amount.
66 payments of 11.62 = $766.92
Finance charge = $766.92 - 400 = 366.92
Cumulative month-interest charges for 66 months
= 66*67/2 = 2211
Cumulative month-interest charges left to be paid after 18 months (66-18=48 months)
= 48*49/2 = 1176
Interest charges saved
= 1176/2211 * 366.92
= $195.16
I too get the second answer and this is the correct one:
A $400 loan is to be paid off in 66 monthly payments of $11.62. The borrower decides to pay off the loan after 18 payments. Use the rule of 78s to find the amount of interest saved.
Answer: $195.16
To find the amount of interest saved using the rule of 78s, we need to understand what the rule of 78s is. The rule of 78s is a formula used to calculate the amount of interest that is allocated to each payment in an installment loan. It assumes that the interest is paid off fully before the principal.
In this case, we have a $400 loan, and we know that the borrower is making 66 monthly payments of $11.62. However, the borrower decides to pay off the loan after 18 payments instead.
To find the amount of interest saved, we can use the formula:
Interest Saved = Total Interest - Interest Remaining
First, we need to find the total interest paid over the course of the loan. We can do this by multiplying the monthly payment by the number of payments:
Total Interest = Monthly Payment * Number of Payments - Loan Amount
Total Interest = $11.62 * 66 - $400
Total Interest = $767.92 - $400
Total Interest = $367.92
Next, we need to find the interest remaining after 18 payments. We can do this by multiplying the monthly payment by the remaining number of payments:
Interest Remaining = Monthly Payment * Remaining Payments - Remaining Principal
Interest Remaining = $11.62 * (66 - 18) - ($400 - $11.62 * 18)
Interest Remaining = $11.62 * 48 - ($400 - $209.16)
Interest Remaining = $557.76 - $190.84
Interest Remaining = $366.92
Now we can calculate the amount of interest saved:
Interest Saved = Total Interest - Interest Remaining
Interest Saved = $367.92 - $366.92
Interest Saved = $1.00
Therefore, the amount of interest saved is $1.00.