Consumer Math - Sequences, The Rule of 78

The series for the Rule of 78, based on this sequence, sums to .

78

Use the example given to determine the percent of total interest owed. After the fifth month of a 12 month loan, the numerator is: {(n+ ) +(n+ ) +(n+ ) +(n+ ) +(n+ )} = , andthe denominator is: {\((n) + (n + 1) + ... + (n +\) )} = .Therefore, the percent to the nearest tenth is (numerator÷denominator)×100= %.

11, 10, 9, 8, 7, 50, 11, 78, 64.1

Use the example given to fill in the missing values. Consider a three-year loan (assume the numbers 1 through 36) for $5,000 with interest at 10% per year. Using standard amortization, the monthly payment is $161.33. In this example, we will not worry about exact or ordinary interest because the total interest to be paid is $808.13. After the fifth month the borrower decides to prepay the whole loan. Under a standard amortization plan the borrower would have paid $198.28 in cumulative interest. However, using the Rule of 78 a lender would calculate the fraction of the total interest based on two series: {(n+35)+(n+34)+(n+33)+(n+32)+(n+31)} and \(\left\{(n)+(n+1)+...+(n+35)\right\}\) If you add 36, 35, 34, 33, and 32, the sum is .If you sum the numbers from 1 to 36, the sum is .The percent to the nearest tenth: (the first sum÷the total sum)×100= %. The lender will multiply this fraction by the total interest.The cumulative interest: (the percentage calculated)×($808.13)=$ . The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78 plan is: $ .

170, 666, 25.5, 206.07, 7.79

For the Rule of 78, for a 12 month period, the last term in the sequence is 12 and the series sums to 78. For an 18 month period, the last term is and the series sum is. For a 24 month period, the last term is and the series sum is. For a 30 month period, the last term is and the series sum is .

18, 171 24, 300 30, 465

Using the example, determine the fraction of total interest paid. After the seventh month of a 12 month loan, the numerator is: {(n+11)+(n+10)+(n+9)+(n+8)+(n+7)+(n+6)+(n+5)}= , and the denominator is: \(\left\{(n)+(n+1)+...+(n+11)\right\}=\) . Therefore, the decimal to the nearest tenth is:(numerator÷denominator)×100=

63, 78, 80.8 (I have no idea why the question appeared like that, also answers are written from left to right)

Good luck guys!

I had a hard time with this one, but just try to understand how to get the answers. Take your time in figuring it out and you'll get there!

A series is:

a summation of quantities whose positions are based upon the natural numbers

The sequence for the Rule of 78 can be written as follows:

{n, n + 1, n + 2, n + 3, n + 4, n + 5, n + 6, n + 7, n + 8, n + 9, n + 10, n + 11}, n = 1

The amount of interest you pay does not depend on the method the lender uses to calculate interest.

False

A sequence is:

an arrangement of quantities whose positions are based upon the natural numbers

A progression is:

an arrangement of quantities whose positions are based upon the natural numbers a summation of quantities based upon a sequence

Use the example given to determine the percent of total interest owed. After the third month of a 12 month loan, the numerator is: {(n+ ) +(n+ ) +(n+ )} = , andthe denominator is: {\((n) + (n + 1) + ... + (n +\) )} = .Therefore, the percent to the nearest tenth is (numerator÷denominator)×100=

11, 10, 9, 33, 11, 78, 42.3