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How much money has to be invested at 4.3% interest compounded continuously to 19000 dollars after 16 ys

User Lughino
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1 Answer

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Final answer:

The formula to calculate the initial investment needed for a future value with continuous compounding is A = Pe^(rt). By plugging in the given values into this formula, you can solve for the principal P to find out how much needs to be invested at a 4.3% interest rate compounded continuously to reach $19,000 in 16 years.

Step-by-step explanation:

To determine how much money needs to be invested at 4.3% interest compounded continuously to grow to $19,000 after 16 years, you can use the continuous compounding formula:

A = Pert

Where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • r is the annual interest rate (decimal).
  • t is the time in years.
  • e is the base of the natural logarithm (approximately equal to 2.71828).

We know that A = $19,000, r = 4.3/100 = 0.043, and t = 16 years. So, we need to solve for P:

19000 = Pe0.043 × 16

Now, you'll want to divide both sides of the equation by e0.043 × 16 to solve for P:

P = 19000 / e0.043 × 16

After calculating the right side of the equation, you will find the amount of money that needs to be invested today.

User Veve
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