Final answer:
After 20 years, at an interest rate of 5.0% compounded continuously, the student will receive approximately $10,873.12 from an initial deposit of $4,000 in the college savings fund.
Step-by-step explanation:
A student has made a deposit of $4,000 in a college savings fund that pays 5.0% interest, compounded continuously, and wishes to know how much will be received after 20 years.
Calculating the future balance of an account with continuously compounded interest uses the formula:
A = P * e^(rt), where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
t = the time the money is invested for, in years.
e = the base of the natural logarithm, approximately equal to 2.71828.
Applying this formula:
A = $4,000 * e^(0.05*20) = $4,000 * e^(1) = $4,000 * 2.71828 = $10,873.12
Therefore, after 20 years, the student will receive approximately $10,873.12 from the college savings fund.