Find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.)
Achieve $225,500 at 8.95% compounded continuously for 8 years, 155 days.
time = 8 years , 155 days
= 8 + 155/365 = 8.42466
x e^(8.4266(.0895)) = 225500
x = $106092.70
The 7th inning needs $35000 in four years to buy new framing equipment. How much should be invested at 4%interest compounded annually.
To find the present value using the present value formula and a calculator, you need two pieces of information: the future value and the interest rate. Here's how you can calculate it:
Step 1: Convert the time into years.
To convert 155 days into years, divide it by 365 (number of days in a year):
155 days ÷ 365 days/year = 0.42466 years (approximately)
Step 2: Find the continuous interest rate (r).
The given interest rate is 8.95% compounded continuously. The continuous interest rate (r) can be found using the formula:
r = ln(1 + i)
Where i is the annual interest rate divided by 100.
r = ln(1 + 8.95%/100)
Using a calculator, calculate the natural logarithm (ln) of 1 + 8.95%/100:
r ≈ ln(1 + 0.0895) ≈ 0.0864 (approximately)
Step 3: Use the present value formula.
The present value formula for continuous compounding is:
PV = FV / e^(rt)
Where PV is the present value, FV is the future value, e is Euler's number (approximately 2.71828), r is the continuous interest rate, and t is time in years.
Let's plug in the values:
PV = 225500 / e^(0.0864 * 8.42466)
Step 4: Calculate the present value using a calculator.
Using a scientific calculator or an online calculator, raise the exponential value e^(0.0864 * 8.42466):
e^(0.0864 * 8.42466) ≈ 2.4458 (approximately)
Now, calculate the present value:
PV ≈ 225500 / 2.4458 ≈ $92,186.86 (approximately)
Therefore, the present value, rounded to the nearest cent, is approximately $92,186.86.