Exponential and log functions
What initial investment at 8.5% compounded continuously for 7 years will accumulate to 50,000?
solve for a
a(e^(.085(7)) = 50000
a = 50000/e^.595 = 27578.13
To find the initial investment that will accumulate to $50,000 with an interest rate of 8.5% compounded continuously for 7 years, you can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = Final amount ($50,000 in this case)
P = Principal amount (initial investment)
e = Euler's number (~2.71828)
r = Annual interest rate (8.5% or 0.085)
t = Time in years (7 years)
To calculate the initial investment, we need to rearrange the formula to solve for P:
P = A / e^(rt)
Now, let's substitute the given values into the equation and solve for P:
P = 50000 / e^(0.085 * 7)
First, calculate e^(0.085 * 7):
e^(0.085 * 7) ≈ 2.71828^(0.595) ≈ 1.81175
Now, substitute this value back into the equation:
P = 50000 / 1.81175
P ≈ $27,562.17
Therefore, the initial investment needed to accumulate to $50,000 at an interest rate of 8.5% compounded continuously for 7 years is approximately $27,562.17.