arthur is 10 years old. tuition for one year at a public two - year college is $3,125. in 8 years, tuition…

arthur is 10 years old. tuition for one year at a public two - year college is $3,125. in 8 years, tuition is expected to increase 32%. arthurs family plans to save for his college costs for 5 years. if the family saves $75 per month, will there be enough money to pay for the expected cost of one year at the college when he is 18? no, they would need to save about $30 more per month to have enough money. no, they would need to save about $15 more per month to have enough money. yes, they could save about $5 less per month and still have enough money. yes, they could save about $30 less per month and still have enough money.

arthur is 10 years old. tuition for one year at a public two - year college is $3,125. in 8 years, tuition is expected to increase 32%. arthurs family plans to save for his college costs for 5 years. if the family saves $75 per month, will there be enough money to pay for the expected cost of one year at the college when he is 18? no, they would need to save about $30 more per month to have enough money. no, they would need to save about $15 more per month to have enough money. yes, they could save about $5 less per month and still have enough money. yes, they could save about $30 less per month and still have enough money.

Answer

Explanation:

Step1: Calculate the expected tuition

The original tuition is $T_0 = 3125$. The percentage increase is $p=32%=0.32$. The expected tuition $T$ after 8 years is calculated using the formula $T = T_0(1 + p)$. So $T=3125\times(1 + 0.32)=3125\times1.32 = 4125$.

Step2: Calculate the total savings

The family saves for $n = 5$ years. Since there are 12 months in a year, the number of months of saving is $m=5\times12 = 60$ months. They save $s = 75$ per month. The total savings $S$ is $S=s\times m=75\times60 = 4500$.

Step3: Analyze the savings - tuition relationship

The total savings $S = 4500$ and the expected tuition $T = 4125$. The difference $\Delta=S - T=4500 - 4125=375$. The extra amount per - month if they had saved for 60 months is $\frac{375}{60}=6.25\approx5$ (rounded to the nearest 5).

Answer:

Yes, they could save about $5 less per month and still have enough money.