Find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.)
Achieve $225,500 at 8.65% compounded continuously for 8 years, 125 days.
8y 125d = 8.347 years, so just solve for P in
P*e^(.0865*8.347) = 225500
Amount = Pert
where P=principal, present value
so
225500=Pe.0865*(8+125/365)
solve for P to get:
109585 (approximately)
To find the present value using the present value formula and a calculator, we can use the formula:
PV = FV * e^(-rt)
where:
PV = present value,
FV = future value (225,500),
r = interest rate (0.0865),
t = time in years (8 years and 125 days = 8.34 years), and
e = mathematical constant (approximately equal to 2.71828).
First, let's calculate the time in years:
8 years + (125 days / 365 days) = 8.34 years
Now, we can plug these values into the formula and solve for PV:
PV = 225,500 * e^(-0.0865 * 8.34)
Using a calculator, we get:
PV ≈ 225,500 * e^(-0.72041) ≈ 225,500 * 0.48751 ≈ 109,936.81
Therefore, the present value, rounded to the nearest cent, is $109,936.81.
To find the present value using the present value formula and a calculator, follow these steps:
Step 1: Convert the time to years by dividing the number of days by 365 (since there are 365 days in a year):
125 days / 365 days = 0.3425 years (rounded to four decimal places).
Step 2: Calculate the present value using the formula:
Present Value = Future Value / (1 + r)^t
Where:
- Future Value is $225,500,
- r is the interest rate expressed as a decimal (8.65% = 0.0865),
- t is the time in years (8.3425 years).
Step 3: Plug in the values into the formula:
Present Value = $225,500 / (1 + 0.0865)^8.3425
Step 4: Use a calculator to evaluate the expression within the parentheses first:
(1 + 0.0865)^8.3425 = 1.58307 (rounded to five decimal places).
Step 5: Divide the future value by the result from Step 4:
Present Value = $225,500 / 1.58307
Step 6: Use a calculator to calculate the present value:
Present Value ≈ $142,523.23 (rounded to the nearest cent).
Therefore, the present value, rounded to the nearest cent, is approximately $142,523.23.