Final answer:
To calculate the present value of $57,000 due in 15 years at 8% compounded continuously, use the formula PV = FV * e^(-rt). Plugging in the values, the correct present value from the given options is $16,206.66.
Step-by-step explanation:
To find the present value of $57,000 due 15 years later at an 8% interest rate compounded continuously, we use the formula for continuous compounding which is:
PV = FV * e-rt
Where:
- PV is the present value
- FV is the future value ($57,000 in this case)
- r is the annual interest rate (0.08 for 8%)
- t is the time in years (15 years)
- e is the base of the natural logarithm (approximately equal to 2.71828)
Plugging in the values, we get:
PV = 57000 * e-(0.08*15) = $57000 * e-1.2
Using a calculator with an exponent function to find e-1.2, we then multiply that by $57,000 to find the present value.
The correct present value from the options given is B) $16,206.66.