Find the present value of $30000 due 14 years later at 7.8%, compounded continuously.
What is 30000 e^(-14(.078)) ?
To find the present value of $30,000 due 14 years later at an interest rate of 7.8% compounded continuously, we can use the formula for continuous compound interest:
PV = A / e^(rt)
Where:
PV = present value
A = future value
e = Euler's number (approximately 2.71828)
r = interest rate
t = time in years
In our case, the future value A is $30,000, the interest rate r is 7.8% (or 0.078 in decimal form), and the time t is 14 years.
Now, let's plug these values into the formula and calculate the present value:
PV = 30,000 / e^(0.078 * 14)
To evaluate e^(0.078 * 14), we can use a calculator or a mathematical software. The result is approximately 0.3702.
Now, let's substitute this value back into the equation:
PV = 30,000 / 0.3702
Performing the division, we get:
PV ≈ $81,000.50
Therefore, the present value of $30,000 due 14 years later, at a continuously compounded interest rate of 7.8%, is approximately $81,000.50.