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.