Stefan invests 7,690 in a retirement account with a fixed annual interest rate of 9% compounded continuously.How long will it take for the account balance to reach 38,858.26 18 years 17 years 15 years 16 years

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Answer 1

To solve this problem, we can use the formula for continuous compounding interest:

Where:-

is the final amount-

is the principal amount (initial investment)-

is the annual interest rate (as a decimal)-

is the time in years-

is the base of the natural logarithmGiven:-

-

(since 9% as a decimal is 0.09)We need to find

.First, plug in the given values into the formula:

Next, solve for

:1. Divide both sides by 7,690:

2. Take the natural logarithm (ln) of both sides to solve for

:

3. Calculate $ \ln(5.05) $:

4. Solve for

:

So, it will take approximately 18 years for the account balance to reach \$38,858.26.Therefore, the correct answer is:

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