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)} = The denominator is: {(n)+(n+1)+...+(n+11)} = Therefore, the fraction is numerator/denominator (to the nearest tenth) =

Answer 1

The fraction of total interest owed is
`(57)/(78)`

The value of it to the nearest tenth is 73.1%

Explanation:

Let us solve it using the rule of 78

∵ The loan = 12 month

∵ The numerator is after 6 month

- Substitute n by 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 of the fraction is 57

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

- substitute n by 1 in each bracket

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

∴ The denominator = {78}

∴ The denominator of the fraction is 78

The fraction of total interest owed is
`(57)/(78)`

Now find the value of the fraction

∵ The fraction =
`(57)/(78)`

∴ Its value = 0.7307692308 × 100%

∴ Its value = 73.07692308%

- Round it to the nearest tenth

∴ Its value = 73.1%

The value of it to the nearest tenth is 73.1%