Following the birth of a child, a parent wants to make an initial investment P 0 that will grow to $70,000 for the child's education at age 19. Interest is compounded continuously at 6%.

Question

Following the birth of a child, a parent wants to make an initial investment P 0 that will grow to $70,000 for the child's education at age 19. Interest is compounded continuously at 6%.

What should the initial investment be? Such an amount is called the present value of $70,000 due 19 years from now.

Answer 1

x e^.06t = 70000

x = 70000/e^(.06(19))
= 22,387.33

Answer 2

Ah, the magical question of saving for education! Let's calculate the present value of that wondrous $70,000.

To find the initial investment, P0, we can use the formula for continuous compound interest:

P0 = A / e^(rt)

Where A is the future value, r is the interest rate, and t is the time in years.

Plugging in the given values:
A = $70,000
r = 0.06 (6% written as a decimal)
t = 19 years

P0 = 70000 / e^(0.06 * 19)

Now, let me find my trusty calculator... *beep boop beep* Ah, there it is!

Calculating... *tick tock tick tock* Voila!

The initial investment, my friend, should be approximately $20,315.31. So make sure to save up that amount to secure your little one's future education. Funny how investing money feels almost as magical as pulling a rabbit out of a hat, isn't it?

Answer 3

To find the initial investment (present value), we need to calculate the amount that needs to be invested today to accumulate to $70,000 in 19 years.

The formula to calculate the present value, P0, of a future value, FV, compounded continuously at an interest rate, r, for a certain period of time, t, is:

P0 = FV / e^(rt)

Where:
P0 = Present Value (Initial Investment)
FV = Future Value ($70,000)
r = Annual interest rate (6% or 0.06 as a decimal)
t = Time in years (19 years)

Step 1: Convert the interest rate from a percentage to a decimal by dividing it by 100: r = 0.06 / 100 = 0.0006.
Step 2: Substitute the values into the formula:

P0 = $70,000 / e^(0.0006 * 19)

Now we need to calculate the exponential term, e^(0.0006 * 19):

e^(0.0006 * 19) ≈ 1.112363

Therefore, the initial investment (present value) should be:

P0 = $70,000 / 1.112363 ≈ $62,904.92

So, the parent should make an initial investment of approximately $62,904.92 to accumulate $70,000 for the child's education at age 19.

Following the birth of a​ child, a parent wants to make an initial investment P 0 that will grow to ​$70,000 for the​ child's education at age 19. Interest is compounded continuously at 6​%.

x e^.06t = 70000

Ah, the magical question of saving for education! Let's calculate the present value of that wondrous $70,000.

To find the initial investment (present value), we need to calculate the amount that needs to be invested today to accumulate to $70,000 in 19 years.

Following the birth of a child, a parent wants to make an initial investment P 0 that will grow to $70,000 for the child's education at age 19. Interest is compounded continuously at 6%.