Cara's total cost for attending the two-year community college is $23,000 x 2 = $<<23000*2=46000>>46,000.
Her total savings from working in summer are $2,800 x 4 = $<<2800*4=11200>>11,200.
So, her total expenses that are covered by savings and scholarships are $11,200 + $10,000 = $<<11200+10000=21200>>21,200.
Her total expenses after savings and scholarships are deducted are $46,000 - $21,200 = $<<46000-21200=24800>>24,800.
The compounding formula is given by A = P (1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.
The equation to find the principal amount, P, is P = A / ((1 + r/n)^(nt)).
Using the given values, the principal amount, P, is P = $24,800 / ((1 + 0.08 / 4)^(4 x 4)).
Therefore, the principal amount that must be deposited is P = $<<24800/((1+0.08/4)^(4*4))=19754>>19,754. Answer: \boxed{19754}.
Cara wants to attend a two-year community college that will cost $23,000 a year. By working during the summer, she can save $2,800 each year for four years. She has identified $10,000 in scholarship money that she would qualify for. Her family is starting a college fund for her by depositing money in an account that will yield 8% compound interest, compounded quarterly for four years. To the nearest thousand, how much must her parents deposit so that their contribution will make up the shortfall in Cara’s plans?(1 point)
1 answer
1 answer