find the present value using the present value formula. Achieve $ 225,500 at 8,95% compounded continuously for 8 years, 135 days.
8 years, 135 days = 8.36986... years
PV e^(.0895(8.36986) = 225500
PV = 106351.80
To find the present value using the present value formula with continuous compounding, we can use the following formula:
PV = Ce^(-rt)
Where:
PV = Present Value
C = Future Value
e = Euler's number (approximately 2.71828)
r = Interest rate per time period
t = Number of time periods
In this case, we have:
C = $225,500
r = 8.95% = 0.0895 (converted to a decimal)
t = 8 years + 135 days = 8 + 135/365 ≈ 8.3699 years
Substituting these values into the formula, we get:
PV = $225,500 * e^(-0.0895 * 8.3699)
To calculate this using a scientific calculator, follow these steps:
1. Enter 0.0895 * 8.3699 and press the multiplication (*) key.
2. Press the '=' key.
3. Write down the result.
4. Press the 'e^x' or 'exp' key (usually located next to the natural logarithm, ln).
5. Enter the result obtained in step 3.
6. Press the '=' key.
7. Write down the final result.
This final result is the present value of the given amount, achieved at a continuous compounding rate of 8.95% over 8 years and 135 days.