Final answer:
Alex's initial deposit of $1500, with an interest rate of 4% compounded quarterly, will grow to approximately $1624.28 in two years, which is short of his $2000 savings goal.
Step-by-step explanation:
Alex needs to know whether his savings account with an initial deposit of $1500 will grow to $2000 in two years with an interest rate of 4% compounded quarterly. To answer this, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (initial deposit).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time in years.
By substituting the given values we get:
A = $1500(1 + 0.04/4)^(4*2)=
A = $1500(1 + 0.01)^(8) =
A = $1500(1.01)^8 ≈ $1500(1.082856) ≈ $1624.28
Therefore, by the end of two years, Alex will have approximately $1624.28, which is not enough to reach his $2000 savings goal.