Andrea Davis's Investment Plan

Investing in a Money Market Account

Andrea Davis plans to invest $600 into a money market account. She wants to find the interest rate that is needed for the money to grow to $1240 in 14 years if the interest rate is compounded continuously.

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%.

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