Find the accumulated value of a CD of $20000 for 3 years at an interest of 3.1% if the money is compounded continously.
P = Po*e^rt.
Po = $20,000.
rt = (3.1%/100%)/yr * 3yrs = 0.093.
P = 20,000*e^0.093 = $21,949.25.
To find the accumulated value of a CD compounded continuously, you can use the formula:
A = P * e^(rt)
Where:
A = Accumulated value
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (as a decimal)
t = Time period (in years)
In this case:
P = $20000
r = 3.1% = 0.031 (since it's given as a percentage, divide by 100)
t = 3 years
Now we can plug the values into the formula:
A = 20000 * e^(0.031 * 3)
To evaluate this expression using a calculator, you can follow the steps:
1. Multiply 0.031 by 3:
0.031 * 3 = 0.093
2. Raise Euler's number (e) to the power of the result:
e^0.093 = 1.097285
3. Multiply the result by the principal amount:
20000 * 1.097285 ≈ 21945.70
Therefore, the accumulated value of a CD of $20000 for 3 years at an interest rate of 3.1% compounded continuously is approximately $21945.70.