Achieve 225,500 at 8/85% compounded continuously for 8 years, 125 days
To calculate continuous compounding you use e^rt.
To achieve $225,500 compounded continuously at an interest rate of 8%, we need to use the continuous compound interest formula:
A = P * e^(rt)
Where:
A is the final amount
P is the principal (initial amount)
e is the base of the natural logarithm (~2.71828)
r is the annual interest rate (in decimal form)
t is the time in years
First, let's convert the given interest rate of 8% to decimal form: 8/100 = 0.08
Now, let's calculate the total time in years, including the fractional part of 125 days:
Time = 8 + (125 / 365) ≈ 8.342
Substitute the values into the continuous compound interest formula:
A = P * e^(rt)
225,500 = P * e^(0.08 * 8.342)
To solve for P (the principal), we need to isolate it on one side of the equation. Divide both sides by e^(0.08 * 8.342):
225,500 / e^(0.08 * 8.342) = P
Using a calculator or computer software with a natural logarithm function, compute e^(0.08 * 8.342) and divide 225,500 by the result to find P.
Please note that the value of e^(0.08 * 8.342) is approximately 2.445.
P ≈ 225,500 / 2.445 ≈ 92,335.12
Therefore, to achieve $225,500 at 8% compounded continuously for 8 years and 125 days, you would need an initial investment (principal) of approximately $92,335.12.