Question

Following the birth of a child, a parent wants to make an initial investment Po that will grow to $50,000 for the child's

education at age 18. Interest is compounded continuously at 7%.
What should the initial investment be? Such an amount is called the present value of $50,000 due 18 years from now.
The present value is about $.
(Do not round until the final answer. Then round to two decimal places as needed.)

Answer 1

The initial investment Po required to grow to $50,000 in 18 years with continuous compounding at a 7% interest rate is approximately $14,223.33.

Step-by-step explanation:

To find out what initial investment Po is required to grow to $50,000 in 18 years with continuous compounding at a 7% interest rate, we use the formula:

P = Pert

Where:

• P is the future value we want to achieve ($50,000)
• r is the annual interest rate (7% or 0.07 as a decimal)
• t is the time in years (18 years)
• e is the base of the natural logarithm (approximately 2.71828)

We are solving for Po, the initial investment.

The formula rearranges to:

Po = P / ert

Substituting the given values:

Po = $50,000 / e(0.07)(18)

Calculate the exponent part:

e(0.07)(18) ≈ e1.26

Approximating: e1.26 is about 3.515

Now, divide $50,000 by this number:

Po ≈ $50,000 / 3.515

≈ $14,223.33

So, the initial investment needed, rounded to two decimal places, is $14,223.33.