find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.)
Achieve $225,500 at 8.35% compounded continuously for 8 years, 125 days.
time = 8 + 125/365 = 8 + .345466 = 8.345466
let the present value be x
x e^(.0835(8.345466)) = 225500
x = $112361.83
To find the present value, we can use the continuous compound interest formula:
PV = A / e^(rt)
Where:
PV = Present Value
A = Future Value or the amount to be achieved
e = Euler's number (approximately 2.71828)
r = Interest rate
t = Time in years
Firstly, convert the time in years to the decimal form. To do this, divide the number of days by 365:
Time in years = (8 years) + (125 days / 365 days per year)
Time in years = 8 + (125 / 365)
Time in years ≈ 8.3425 years
Now, we can substitute the given values into the formula:
PV = 225500 / e^(0.0835 * 8.3425)
Using a calculator, calculate the exponential part of the equation:
e^(0.0835 * 8.3425) ≈ 2.082026
Now, divide the future value by the exponential value:
PV = 225500 / 2.082026
Using a calculator, divide 225500 by 2.082026:
PV ≈ $108,320.22
Therefore, the present value, rounded to the nearest cent, is approximately $108,320.22.