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?\nno, they would need to save about $30 more per month to have enough money.\nno, they would need to save about $15 more per month to have enough money.\nyes, they could save about $5 less per month and still have enough money.\nyes, 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?\nno, they would need to save about $30 more per month to have enough money.\nno, they would need to save about $15 more per month to have enough money.\nyes, they could save about $5 less per month and still have enough money.\nyes, they could save about $30 less per month and still have enough money.

Answer

Explanation:

Step1: Calculate the expected tuition cost

The initial tuition is ( $3125 ). It increases by ( 32% ). The formula for the new amount after a percentage increase is ( A = P(1 + r) ), where ( P=$3125 ), ( r = 0.32 ). [ \begin{align*} A&=3125\times(1 + 0.32)\ &=3125\times1.32\ &=3125\times(1+\frac{32}{100})\ &=3125+\frac{3125\times32}{100}\ &=3125 + 1000\ &=$4125 \end{align*} ]

Step2: Calculate the amount saved per month

The family saves for ( 5) years. Since there are ( 12) months in a year, the number of months ( n=5\times12 = 60) months. If they save ( $75) per month, the total amount saved ( S=75\times60=$4500)

Step3: Analyze the difference

The amount saved ( S = 4500) and the expected tuition ( A=4125) The difference ( d=4500 - 4125=$375) The extra amount per month ( x=\frac{375}{60}=6.25\approx5) (approximate value)

Answer:

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