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Question
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)
$
To calculate the amount her parents must deposit, we need to determine the total cost of her community college education and subtract the money she will save, the scholarship money, and the interest earned from the college fund.
Total cost of community college education for 2 years = $23,000/year * 2 years = $46,000
Total money saved by Cara through summer work = $2,800/year * 4 years = $11,200
Total scholarship money = $10,000
Total interest earned from the college fund = Principal * (1 + interest rate/number of compounding periods)^(number of compounding periods * number of years)
Assuming her parents want to deposit x dollars, we have:
Principal = x
Interest rate = 8% = 0.08
Number of compounding periods = 4 (compounded quarterly)
Number of years = 4
Total interest earned from the college fund = x * (1 + 0.08/4)^(4*4) - x
Now, we can calculate the amount her parents must deposit:
Total parents' deposit = Total cost of community college education - Total money saved - Total scholarship money - Total interest earned from the college fund
= $46,000 - $11,200 - $10,000 - [x * (1 + 0.08/4)^(4*4) - x]
To the nearest thousand, her parents must deposit this amount.