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
I really would like to get help with this problem.
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 = the future value or the amount Stacy wants to have in three years ($3,000)
P = the principal or the amount she needs to invest today
r = the annual interest rate expressed as a decimal (8% = 0.08)
n = the number of times interest is compounded per year (annually)
t = the number of years (3 years)
We can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Let's substitute the given values into the formula:
P = $3,000 / (1 + 0.08/1)^(1*3)
P = $3,000 / (1 + 0.08)^3
P = $3,000 / (1.08)^3
P = $3,000 / 1.259712
P ≈ $2,381.49
Therefore, Stacy needs to invest approximately $2,381.49 today to have $3,000 in three years.
Thus, the correct option is (a) $2,381.49.