Find the present value of $26997.18 due in 3 yr at an interest rate of 10%/year compounded continuously.
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26997.18 = PV(1.10)^10
26997.18/(1.10)^10 = PV
26997.18/2.59374 = PV
10408.59 =PV
again, I disagree with angela' s answer
PV = 26997.18 e^(-.1(3))
= 26997.18 e^-.3
= 20,000.00
To find the present value of an amount due in the future, compounded continuously, we can use the formula:
PV = A / e^(rt)
Where:
PV = Present value
A = Amount due in the future
r = Interest rate (in decimal form)
t = Time period in years
e = Euler's number (approximately 2.71828)
In this case, the amount due in 3 years is $26,997.18, and the interest rate is 10% per year compounded continuously.
First, we need to convert the interest rate into decimal form. Divide the interest rate by 100:
10% / 100 = 0.10
Next, substitute the values into the formula and calculate the present value:
PV = 26997.18 / e^(0.10 * 3)
Now, calculate e^(0.10 * 3) first:
e^(0.10 * 3) ≈ 2.213
Now, substitute this value back into the original formula:
PV ≈ 26997.18 / 2.213
By calculating this, we find that the present value is approximately $12,188.20