Find the present value, using the present value formula. (Round your answer to the nearest cent.)
Achieve $225,500 at 8.45% compounded continuously for 8 years, 145 days.
To find the present value using the present value formula, we need to use the formula:
PV = FV / (1 + r)^t
Where:
PV = present value
FV = future value
r = interest rate
t = time in years
First, let's convert the time in years and days to years only. 145 days is approximately 0.397 years (145 days / 365 days per year).
Now, let's substitute the given values into the formula:
PV = $225,500 / (1 + 0.0845)^8.397
Now, let's calculate the present value using a calculator:
PV = $225,500 / (1.0845)^8.397
≈ $122,903.92
Therefore, the present value, rounded to the nearest cent, is approximately $122,903.92.
To find the present value using the present value formula, we'll need to use the formula for continuous compound interest:
PV = A / e^(rt)
where:
PV is the present value
A is the future value (in this case, $225,500)
e is the base of the natural logarithm (approximately 2.71828)
r is the interest rate per year (in decimal form, in this case, 8.45% or 0.0845)
t is the time in years (in this case, 8 years and 145 days)
First, we need to convert the time in years. There are 365 days in a year, so 145 days is approximately 0.3973 years (145/365 = 0.3973).
Now we can substitute the values into the formula and calculate the present value:
PV = 225500 / e^(0.0845 * (8 + 0.3973))
Using a calculator, we have:
PV ≈ 225500 / e^(0.0845 * 8.3973)
≈ 225500 / e^0.714835
≈ 225500 / 2.045
≈ $110,328.79
Therefore, the present value, rounded to the nearest cent, is $110,328.79.