find the present value using the present value formula. Achieve $ 225,500 at 8.65% compounded continusly for 8 years 155 days
To find the present value using the formula for continuous compounding, we can use the following formula:
PV = A / e^(r*t)
Where:
PV = Present Value
A = Future Value
r = Annual interest rate (in decimal form)
t = Time in years
First, we need to convert the time into years. 8 years 155 days is equivalent to 8.42671233 years.
Next, we can substitute the values into the formula:
PV = 225,500 / e^(0.0865*8.42671233)
Using a calculator, we can compute the value of e^(0.0865*8.42671233) to be approximately 2.4515.
Now we can plug this value into the formula and calculate the present value:
PV = 225,500 / 2.4515
Simplifying, we have:
PV ≈ $92,058.21
Therefore, the present value is approximately $92,058.21
To find the present value using the present value formula, you need to use the formula for compound interest in continuous compounding. The formula is:
P = A / e^(rt)
Where:
P is the present value
A is the future value (the amount you want to achieve)
e is the base of the natural logarithm (approximately 2.71828)
r is the interest rate (expressed as a decimal)
t is the time in years
Now let's calculate the present value.
First, we need to convert the time in years and days to a decimal representation of years. Since there are 365 days in a year, we can calculate the decimal representation of 155 days as follows:
Decimal representation of 155 days = 155 / 365 ≈ 0.4247
So, the total time in years is 8 years + 0.4247 years = 8.4247 years.
Now plug in the values into the formula:
P = 225,500 / e^(0.0865 * 8.4247)
Next, calculate the exponent:
0.0865 * 8.4247 ≈ 0.7294
Now calculate e^(0.7294). Using a calculator, you find that e^(0.7294) ≈ 2.0735.
Finally, divide the future value (225,500) by 2.0735 to find the present value:
P ≈ 225,500 / 2.0735 ≈ $108,748.52
Therefore, the present value using the present value formula is approximately $108,748.52.