To calculate the principal amount that Wesley needs to deposit in a savings account that earns 10% interest compounded continuously, we can use the following formula:
FV = PV * e^(r*t)
where:
FV is the future value of the investment, which is the cost of the machine plus the interest earned.
PV is the present value of the investment, which is the principal amount that Wesley needs to deposit.
r is the annual interest rate, which is 10% or 0.1.
t is the time period, which is 1 year.
We can rearrange the formula to solve for PV:
PV = FV / e^(r*t)
Substituting the given values, we get:
PV = $10,000 / e^(0.1*1)
PV = $9,048.73
Therefore, Wesley needs to deposit $9,048.73 as principal in a savings account that earns 10% interest compounded continuously to have enough money in 1 year to buy the machine.
I hope this helps!