Baako has invested $75,000 in a trust fund at 9% for his child's college education. His child will draw $30,000 per year for four years, starting at the end of year 7. What will be the amount that will be left over in the education fund at the end of year 10, just after the child has withdrawn the fourth time?

$40358

calculations please

To determine the amount that will be left over in the education fund at the end of year 10, just after the child has made the fourth withdrawal, we need to calculate the future value of the trust fund.

Here's how you can calculate it step by step:

1. Calculate the interest earned on the investment each year:
- Principal (initial investment): $75,000
- Annual interest rate: 9%
- Interest earned each year: Principal x Interest rate = $75,000 x 9% = $6,750

2. Calculate the amount remaining after each withdrawal:
- After the first withdrawal (end of year 7): Remaining amount = Principal + Interest earned - Withdrawal amount = $75,000 + $6,750 - $30,000 = $51,750
- After the second withdrawal (end of year 8): Remaining amount = Previous remaining amount + Interest earned - Withdrawal amount = $51,750 + $6,750 - $30,000 = $28,500
- After the third withdrawal (end of year 9): Remaining amount = Previous remaining amount + Interest earned - Withdrawal amount = $28,500 + $6,750 - $30,000 = $5,250
- After the fourth withdrawal (end of year 10): Remaining amount = Previous remaining amount + Interest earned - Withdrawal amount = $5,250 + $6,750 - $30,000 = -$18,000

The negative remaining amount indicates that there will be a deficit of $18,000 at the end of year 10, just after the child has made the fourth withdrawal.