Question

A college raises its tuition in each of three consecutive years. if the percent increase was 4​%, ​9%, and ​6%, determine the overall percent increase at the end of the​ three-year period.

Answer 1

The overall percent increase in tuition over three years with increases of 4%, 9%, and 6% is calculated by compounding each annual increase, not by simple addition. The calculation involves multiplying the original tuition by (1 + 0.04) x (1 + 0.09) x (1 + 0.06) and then determining the percent increase from the original tuition.

Step-by-step explanation:

To determine the overall percent increase in tuition after three consecutive years with increases of 4%, 9%, and 6%, we need to apply each percentage increase one after the other. Rather than simply adding up the percentages, we need to compound them since each percent increase is applied to the new tuition amount.

Mathematically, we can calculate this as follows:

• First year: New Tuition = Original Tuition x (1 + 4/100)
• Second year: New Tuition = First Year's New Tuition x (1 + 9/100)
• Third year: New Tuition = Second Year's New Tuition x (1 + 6/100)

We can generalize this using a formula:

Final Tuition = Original Tuition x (1 + 0.04) x (1 + 0.09) x (1 + 0.06)

Now, we calculate the overall increase percentage:

Overall Increase = (Final Tuition / Original Tuition - 1) x 100%

The overall percent increase is the final result obtained from the calculation above.