Andrea Davis's Investment Plan
Investing in a Money Market Account
When money is compounded continuously, the formula used is:
A = P*e^(rt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (the initial amount of money)
r = the annual interest rate (in decimal form)
t = the time the money is invested for in years
Given that P = $600, A = $1240, and t = 14 years, we can now solve for the interest rate r.
Calculating the Interest Rate
Using the formula A = P*e^(rt), we substitute the values:
1240 = 600*e^(14r)
Dividing both sides by 600:
e^(14r) = 1240/600 = 2.067
Taking the natural logarithm (ln) of both sides:
14r = ln 2.067
r = ln 2.067 / 14 ≈ 0.052
Therefore, the interest rate needed for Andrea's money to grow to $1240 in 14 years when compounded continuously is approximately 5.2%.
What is the interest rate needed for Andrea's money to grow to $1240 in 14 years when compounded continuously?
The interest rate needed is 5.2%.