Stacy requires $3,000 in three years to make a down payment on a new car. She will receive 8% compounded annually for the three years. How much must she invest today to have the $3,000 in three years?
(a) $ 2,381.49 (b) $ 2,419.35 (c) $ 2,000.00 (d) $ 2,500.00 (e) $ 2,250.00
To find out how much Stacy must invest today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment
P is the principal amount (the initial investment)
r is the annual interest rate (as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
In this case, Stacy wants to have $3,000 in three years and will receive 8% interest compounded annually. So, we can plug in the values into the formula:
$3,000 = P(1 + 0.08/1)^(1*3)
Simplifying the equation:
$3,000 = P(1.08)^3
To isolate P, divide both sides of the equation by (1.08)^3:
P = $3,000 / (1.08)^3
Now, calculate the value of (1.08)^3:
(1.08)^3 = 1.259712
Substitute this value back into the equation:
P = $3,000 / 1.259712
P ≈ $2,381.49
Therefore, Stacy must invest approximately $2,381.49 today in order to have $3,000 in three years.
So, the correct answer is (a) $2,381.49.