lee willis needs to save $16,000 to open up a hair salon in 5 years. what lump sum must Lee deposit today in order to have $16,000 in 5 years? Lee can earn 7.25% interest compounded quarterly
needs x where
x(1+.0725/4)^(4*5) = 16000
To find the lump sum that Lee must deposit today to have $16,000 in 5 years with an interest rate of 7.25% compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value (amount Lee wants to have in 5 years) = $16,000
P = the initial principal (lump sum deposit)
r = annual interest rate (7.25% or 0.0725 as a decimal)
n = number of compounding periods per year (quarterly, so n = 4)
t = number of years (5 years)
Let's solve for P:
16,000 = P(1 + 0.0725/4)^(4 * 5)
To simplify the calculation, let's first simplify the right side of the equation:
16,000 = P(1 + 0.018125)^(20)
16,000 = P(1.018125)^(20)
Now we can solve for P by dividing both sides of the equation by (1.018125)^(20):
P = 16,000 / (1.018125)^(20)
Using a calculator, we can find that approximately:
P ≈ $11,183.63
Therefore, Lee must deposit approximately $11,183.63 today in order to have $16,000 in 5 years with an interest rate of 7.25% compounded quarterly.