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Find the present value of $40,000 due 10 years later at 6%, compounded continuously.

User Obchardon
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Final answer:

The present value of $40,000 due in 10 years at a 6% interest rate, compounded continuously, is calculated using the continuous compounding formula. The present value is found to be approximately $21,952.

Step-by-step explanation:

To find the present value of $40,000 due 10 years later at 6%, compounded continuously, we use the formula for continuous compounding, which is:

PV = Pe-rt

where :

  • PV is the present value
  • P is the future value
  • r is the annual interest rate (as a decimal)
  • t is the time in years
  • e is the base of the natural logarithm (approximately equal to 2.71828)

Substituting the given values into the formula, we get:

PV = $40,000 x e-0.06 x 10

Calculating the exponent :

PV = $40,000 x e-0.6

Using a calculator to find the value of e-0.6, we get:

PV = $40,000 x 0.5488

Finally, calculate the present value:

PV = $21,952

Therefore, the present value of $40,000 due in 10 years at a 6% interest rate, compounded continuously, is approximately $21,952.

User Bergey
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