Question

Determine the fraction of total interest owed using the rule of 78.

After the six month of a 12 month loan, the numerator is: {(n+11)+(n+10)+(n+9)+(n+8)+(n+7)+(n+6)) =
A.78
B. 57
C.51

The denominator is: ((n)+(n+1)+...+(n+11)} =
A.51
B.78
C.57

Therefore, the fraction is numerator/denominator (to the nearest tenth) =
A.73.1%
B.65.4%
C.136.8%

Answer 1

The numerator is 57 ⇒ B

The denominator is 78 ⇒ B

The value of the fraction is 73.1% ⇒ A

Explanation:

Let us solve it step by step

∵ The loan is 12 month

∵ The numerator is after 6 month

- Put n = 1 in each bracket

∴ The numerator = {(1 + 11) + (1 + 10) + (1 + 9) + (1 + 8) + (1 + 7) + (1 + 6)}

∴ The numerator = {12 + 11 + 10 + 9 + 8 + 7}

∴ The numerator = {57}

The numerator is 57

∵ The denominator = {(n) + (n + 1) + (n + 2) + .......... + (n + 11)}

- Do the same as the numerator put n = 1

∴ The denominator = {1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}

∴ The denominator = {78}

The denominator is 78

Now find the value of the fraction

∵ The fraction =
`(57)/(78)`

∴ Its value = 0.730769230

- Multiply it by 100%

∴ Its value = 0.730769230 × 100% = 73.0769230%

- Round it to the nearest tenth

∴ Its value = 73.1%

The value of the fraction is 73.1%