To calculate the required principal amount that Luca needs to deposit in the savings account to have enough money to buy the machine in 1 year, we can use the formula for compound interest:
A = P * e^(rt)
where:
A = final amount ($6,000.00)
P = principal amount (to be calculated)
r = annual interest rate (1% or 0.01)
t = time in years (1)
Therefore, the equation becomes:
$6,000.00 = P * e^(0.01*1)
$6,000.00 = P * e^0.01
$6,000.00 = P * 1.01005016708
P = $6,000.00 / 1.01005016708
P ≈ $5,940.98
Therefore, Luca needs to deposit approximately $5,940.98 as principal in the savings account to have enough money in 1 year to buy the machine.
