To determine the best answer choice for the question, let's follow the detailed steps for calculating the cost of college tuition after one year, given an annual increase rate of 5%.
1. Identify the initial cost of tuition:
The initial cost of tuition is [tex]$6,955.
2. Identify the rate of increase:
The rate of increase is 5%, or 0.05 in decimal form.
3. Determine the time period:
The time period we are considering is one year.
4. Use the formula for compound interest to calculate the new cost:
The formula to calculate the future value given a constant percentage increase is:
\[ \text{Final Cost} = \text{Initial Cost} \times (1 + \text{rate})^{\text{time}} \]
Plugging in the values:
- Initial Cost = $[/tex]6,955
- Rate = 0.05
- Time = 1 year
[tex]\[ \text{Final Cost} = 6,955 \times (1 + 0.05)^1 \][/tex]
5. Calculate the expression step-by-step:
- First, add 1 to the rate: [tex]\( 1 + 0.05 = 1.05 \)[/tex]
- Next, raise this sum to the power of the time period (which is 1 in this case): [tex]\( 1.05^1 = 1.05 \)[/tex]
- Finally, multiply the initial cost by this result:
[tex]\[ 6,955 \times 1.05 = 7,302.75 \][/tex]
Thus, the cost of college tuition after one year, accounting for a 5% increase, will be \[tex]$7,302.75.
Given the answer choices:
- A. $[/tex]6,955
- B. [tex]$7,342
- C. $[/tex]7,596
- D. [tex]$7,235
The closest and most accurate option matching our calculated value is $[/tex]7,342.
Therefore, the best answer is:
B. $7,342
