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 14 month period, the last term is
and the series sum is
.

For a 16 month period, the last term is
and the series sum is
.

For a 20 month period, the last term is
and the series sum is
.

1 answer

The Rule of 78, also known as the sum-of-the-digits method, is used in calculating the prepayment penalties for loans. In this method, the sum of digits of the total number of payments (months, in this case) is used to calculate the interest on a loan.

To determine the last term and the series sum for different periods, you can calculate as follows:

  1. For a 12-month period:

    • The last term in the sequence: 12
    • The series sums to: 78
  2. For a 14-month period:

    • The last term in the sequence is calculated as: \( \text{last term} = 14 \)
    • The series sum is calculated as: \[ \text{Series sum} = 14 + 13 + 12 + ... + 1 = \frac{14 \times (14 + 1)}{2} = \frac{14 \times 15}{2} = 105 \]
  3. For a 16-month period:

    • The last term in the sequence: 16
    • The series sum is calculated as: \[ \text{Series sum} = 16 + 15 + 14 + ... + 1 = \frac{16 \times (16 + 1)}{2} = \frac{16 \times 17}{2} = 136 \]
  4. For a 20-month period:

    • The last term in the sequence: 20
    • The series sum is calculated as: \[ \text{Series sum} = 20 + 19 + 18 + ... + 1 = \frac{20 \times (20 + 1)}{2} = \frac{20 \times 21}{2} = 210 \]

So the final results are:

  • For a 14-month period: Last term is 14, Series sum is 105.
  • For a 16-month period: Last term is 16, Series sum is 136.
  • For a 20-month period: Last term is 20, Series sum is 210.
Similar Questions
    1. answers icon 1 answer
    1. answers icon 3 answers
  1. the first term of a sequence of numbers is 24.the term-to-term rule of this sequence is to 'add 8' josie says "No number in this
    1. answers icon 1 answer
  2. Write a rule for the sequence: 3, 9, 27, 81, ...Find the next three terms of the sequence: 2, 5, 8, 11, ... What is the 10th
    1. answers icon 0 answers
more similar questions