Question

A college raises its tuition in each of three consecutive years. If the percent increase by 5%, 9%, and 7%, determine the overall percent increase at the end of the three-year period?

Answer 1

The overall percentage increase is 22.5%.

step-by-step explanation

Percentage increase in the first year=5%

Percentage increase in the second year=9%

Percentage increase in the third year=7%

we have to calculate the overall percentage increase

Let  the initial tuition fees be x

tuition fees after three years=

=$x\times \frac{100+a}{100} \times\frac{100+b}{100}\times \frac{100+c}{100} \\=x\times \frac{105}{100} \times\frac{109}{100} \times\frac{107}{100} \\\\=x\times \frac{1224615}{1000000} \\=x\times\frac{122.4625}{100} \\=x\times\frac{100+22.4625}{100}$

The overall percentage increase is 22.5%.

Answer 2

The overall increment at the end of the three-year period is 22.5%

The increments are given as:

$\mathbf{Year\ 1 =5\%}$

$\mathbf{Year\ 2 =9\%}$

$\mathbf{Year\ 3 =7\%}$

So, the overall increment is calculated as:

$\mathbf{Overall = (1 + Year\ 1) \times (1 + Year\ 2) \times (1 + Year\ 3) -100\%}$

Substitute known values

$\mathbf{Overall = (1 + 5\%) \times (1 + 9\%) \times (1 + 7\%) -100\%}$

Express as decimals

$\mathbf{Overall = (1 + 0.05) \times (1 + 0.09) \times (1 + 0.07) -100\%}$

$\mathbf{Overall = (1.05) \times (1.09) \times (1.07) -100\%}$

Multiply

$\mathbf{Overall = 1.224615 -100\%}$

Express as percentage

$\mathbf{Overall = 122.4615\% -100\%}$

Subtract

$\mathbf{Overall = 22.4615\%}$

Approximate

$\mathbf{Overall = 22.5\%}$

Hence, the overall increment is 22.5%

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