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Use the example above and determine the fraction of total interest owed. After the fifth month of a 12-month loan: the numerator is: {(n + ) + (n + ) + (n + ) + (n + ) + (n + )} = , and the denominator is: {(n) + (n + 1) + ... + (n + )} = . Therefore, the fraction is numerator/denominator (to the nearest tenth) = %.

Answer :

MrRoyal

The fraction of total interest owed after the fifth month of a 12-month loan is 64.1%

How to determine the fraction of interest owed?

From the question, we have the following parameters

  • The numerator is given as:  {(n+11)+(n+10)+(n+9)+(n+8)+(n+7)}
  • The denominator is given as: {(n)+(n+1)+...+(n+11)}

After the fifth month, the equation of the numerator is:

Numerator = (1+11)+(1+10)+(1+9)+(1+8)+(1+7)

Numerator = 50

The equation of the denominator is:

Denominator = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Denominator = 78

The fraction of total interest is then calculated using:

Fraction = Numerator/Denominator

This gives

Fraction = 50/78

Express as percentage

Fraction = 64.1%

Hence, the fraction of total interest owed after the fifth month of a 12-month loan is 64.1%

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