Question Watch Video Show Examples Jason is going to invest $\$ 16,000$ and leave it in an account for 7 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Jason to end up with $\$ 26,000$ ? Answer Attempt1 1 out of 2
Solution
Step 1 ：Given that Jason is going to invest $16,000 and leave it in an account for 7 years. He wants to end up with $26,000. We are to find the interest rate required for this to happen assuming the interest is compounded continuously.
Step 2 ：The formula for continuous compound interest is \(A = P * e^{rt}\), where \(A\) is the final amount, \(P\) is the principal amount, \(r\) is the interest rate, and \(t\) is the time in years.
Step 3 ：We can rearrange this formula to solve for \(r\): \(r = \frac{ln(A/P)}{t}\).
Step 4 ：Substitute the given values into the formula: \(P = 16000\), \(A = 26000\), and \(t = 7\).
Step 5 ：Solving for \(r\) gives us \(r = 0.06935825939738584\).
Step 6 ：To convert this to a percentage, we multiply by 100, giving us \(r = 6.9\%\).
Step 7 ：Final Answer: The interest rate required for Jason to end up with $26,000 after 7 years is approximately \(\boxed{6.9\%}\).
