Question

Determine the amount of money you need to invest to have $18,000 dollars in 2 years if you Invest it at 20% annual Interest, compounded

continuously.
$28,852.84
$17,294.21
$12,065.76
$133,033.01

Answer 1

To have $18,000 in 2 years with a 20% annual interest rate compounded continuously, you need to invest approximately $12,065.76.

Step-by-step explanation:

To determine the amount of money you need to invest to have $18,000 in 2 years with a 20% annual interest rate compounded continuously, we can use the formula:

A = P * e^(rt)

Where:

• A is the future value (in this case $18,000)
• P is the principal amount we need to find
• e is the mathematical constant approximately equal to 2.71828
• r is the interest rate (20% = 0.20)
• t is the time in years (2 years)

Substituting the values into the formula:

18,000 = P * e^(0.20*2)

Simplifying:

18,000 = P * e^(0.40)

P = 18,000 / e^(0.40)

Using a calculator to evaluate the exponential term:

P ≈ 12,065.76

Therefore, you need to invest approximately $12,065.76 to have $18,000 in 2 years.