Final answer:
The present value of $60,000 due 14 years from now at a 6.7% continuous compounding rate is approximately $23,481.24. This calculation uses the continuous compounding formula PV = Pe-rt, where P is the future value, r is the annual interest rate, and t is the time in years.
Step-by-step explanation:
To find the present value of $60,000 due 14 years later at a continuous compounding rate of 6.7%, we use the continuous compounding formula:
PV = Pe-rt
Where:
- PV = Present Value
- P = Future Value ($60,000 in this case)
- r is the annual interest rate (expressed as a decimal, so 6.7% becomes 0.067)
- t = time in years (14 years in this case)
- e is the base of the natural logarithm, approximately equal to 2.71828
Plugging the numbers into the formula:
PV = $60,000 * e-0.067*14
Calculating the exponential part gives us:
PV = $60,000 * e-0.938
PV = $60,000 * 0.39135393 (rounded to 8 decimal places)
The present value is approximately $23,481.24 when all calculations are done.