Question

Alex is saving money for a new car. He would like to have $2000 saved two years from now. If his savings account earns 4% compounded quarterly and he starts initially with a deposit of $1500, will he have reached his goal in two years?

Answer 1

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.