Find the present value of $9500 in 6 1/2 years if money earns 7.5% compounded continuously.
value = 9500 e^6.5(.075)
= 9500 e^.4875 = $15468.83
Hmm. I think the present value of the 9500 is v such that
9500 = v*e^.4875
v = 9500*e^-.4875 = 5834.52
To find the present value of an amount in the future with continuous compounding, we can use the formula:
PV = A / e^(rt)
Where:
PV = Present Value
A = Future Amount
e = Euler's Number (approximately 2.71828)
r = Interest Rate per year (as a decimal)
t = Time in years
In this case, the future amount (A) is $9,500, the interest rate (r) is 7.5% or 0.075 as a decimal, and the time (t) is 6.5 years.
Now, let's plug these values into the formula:
PV = 9500 / e^(0.075 * 6.5)
To calculate this using a standard calculator, follow these steps:
1. Enter 0.075 * 6.5 and calculate the result.
(0.075 * 6.5 = 0.4875)
2. Press the "e^x" or "exp" button on your calculator and enter the result from step 1.
(e^0.4875 ≈ 1.628)
3. Divide the original amount by the result from step 2.
(9500 / 1.628 ≈ 5835.92)
The present value of $9500 in 6 1/2 years, with continuous compounding at a 7.5% interest rate, is approximately $5835.92.