Find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.)
Achieve $225,500 at 8.55% compounded continuously for 8 years, 125 days.
I do not know present value formula, using head
125/365 = .34247
so t = 8.34247
A = p e^rt
225,500 = p e^.0855 (8.34247)
ln 225,500 = ln p + .71328
ln p = 11.6128
p = $110,502.72
To find the present value using the present value formula, we can use the formula:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Interest rate per compounding period
n = Number of compounding periods
1. Convert the time period 8 years, 125 days into decimal form. Since there are 365 days in a year, we can calculate the total number of days in 8 years and 125 days as follows:
8 years = 8 * 365 = 2,920 days
125 days = 125
Total number of days = 2,920 + 125 = 3,045 days
2. Next, convert the time period in days into years. Since the interest rate is provided annually, we need to convert the time period in years. To do this, divide the total number of days by 365:
3,045 days / 365 = 8.34 years (approximately)
3. Now we can substitute the values into the formula:
PV = FV / (1 + r)^n
PV = $225,500 / (1 + 0.0855)^8.34
4. Use a calculator to evaluate the right-hand side of the equation:
PV ≈ $225,500 / (1.0855)^8.34
First, calculate (1.0855)^8.34, then divide $225,500 by the result:
PV ≈ $225,500 / 1.918822
5. Divide $225,500 by 1.918822 to find the present value:
PV ≈ $117,466.34
Therefore, the present value, rounded to the nearest cent, is approximately $117,466.34.