A small community college is hoping to raise enough funds to put together an endowment in which the scholarships will be paid for by only the interest earned from the endowment. Assuming they can earn an average of 7.50% for the APR and that only the interest would be spent each year, how much money would need to be invested initially in the endowment account as a lump sum in order pay for $80,000 in scholarships?
I = PRT
80,000 = P * 0.075 * 1
80,000 / 0.075 = P
1,066,666.67 = P
To calculate the initial amount needed in the endowment account to pay for $80,000 in scholarships, you need to determine how much interest will be earned each year.
First, calculate the interest earned each year using the average annual percentage rate (APR) of 7.50%. Convert the APR to a decimal by dividing it by 100: 7.50 / 100 = 0.075.
Next, multiply the interest rate by the amount to be invested initially: 0.075 * initial amount = interest earned.
Since the scholarships are paid from the interest earned, the interest earned should be equal to $80,000: interest earned = $80,000.
Now, we can solve the equation to find the initial amount needed in the endowment account:
0.075 * initial amount = $80,000
Divide both sides of the equation by 0.075 to isolate the initial amount:
initial amount = $80,000 / 0.075
Calculate the initial amount needed:
initial amount = $1,066,666.67
Therefore, the small community college would need to invest a lump sum of approximately $1,066,666.67 initially in the endowment account to pay for $80,000 in scholarships if they can earn an average of 7.50% APR.