How much money has to be invested at 3.3% interest compounded continuously to have $45,000 after 19 years?
45000 = P*e^(.033*19)
P = 24038.60
To find out how much money needs to be invested at 3.3% interest compounded continuously to have $45,000 after 19 years, you can use the continuous compound interest formula:
A = P * e^(rt)
In this case, A represents the future value ($45,000), P represents the initial amount to be invested, r represents the annual interest rate (3.3% expressed as a decimal, which is 0.033), t represents the time in years (19), and e represents Euler's number (approximately 2.71828).
To solve for P, we rearrange the formula:
P = A / e^(rt)
Substituting the given values:
P = $45,000 / e^(0.033 * 19)
Now we can calculate the value of e^(0.033 * 19):
e^(0.033 * 19) ≈ 1.607258
Plugging this value back into the formula:
P = $45,000 / 1.607258
P ≈ $27,969.60
Therefore, approximately $27,969.60 needs to be invested at 3.3% interest compounded continuously to have $45,000 after 19 years.
To find the initial investment amount required at a continuous interest rate of 3.3% to accumulate $45,000 after 19 years, you can use the formula for compound interest:
A = P * e^(rt)
Where:
A = the final amount
P = the initial investment amount
e = the base of the natural logarithm (approximately 2.71828)
r = the interest rate (in decimal form)
t = the time period (in years)
In this case, we have:
A = $45,000
r = 3.3% = 0.033
t = 19
Let's plug in the values and solve for P:
45,000 = P * e^(0.033 * 19)
Now, we need to isolate P on one side of the equation. Divide both sides by e^(0.033 * 19):
P = 45,000 / e^(0.033 * 19)
Now let's calculate the value of e^(0.033 * 19) (using a calculator or approximation):
e^(0.033 * 19) ≈ 1.6834
Therefore:
P ≈ 45,000 / 1.6834
P ≈ $26,727.24
So, approximately $26,727.24 should be invested at 3.3% interest compounded continuously to accumulate $45,000 after 19 years.