In order to provide an ongoing scholarship award of $4,000 each year starting one year from now, the Bradford family needs to provide an initial investment that will generate enough interest to cover the annual scholarship amount.
Since the funds will be invested at 8% compounded continuously, we can use the formula for continuous compound interest:
A = P * e^(rt)
where:
A = amount of money accumulated after n years, including interest
P = principal amount (initial investment)
e = Euler's number (approximately equal to 2.71828)
r = annual interest rate (8% or 0.08)
t = time in years
Since the scholarship will start one year from now, we need to calculate the present value of $4,000 per year starting in year 1. We can represent this present value as:
PV = $4,000 / e^0.08
PV = $4,000 / 2.71828^0.08
PV = $4,000 / 1.08329
PV = $3,693.39
Therefore, the Bradford family needs to provide an initial investment of approximately $3,693.39 to the college in order to fund an ongoing scholarship award of $4,000 each year, starting one year from now, with an 8% continuous compound interest rate.
The Bradford family wants to establish an ongoing scholarship award at a college. each year in June $4000 will be awarded starting one year from now. what amount must the Bradford provide the college assuming funds will be invested at 8% compounded continuously
1 answer
1 answer