Zeke deposited $3,000 at 5.4% interest, compounded continuously, when he was 18 years old. How much will be in the account when he is 30 years old if he made no other deposits or withdrawals?

To calculate the amount in the account when Zeke is 30 years old, we can use the formula for continuous compounding interest:

\[
A = P \cdot e^{rt}
\]

Where:
- $ A $ is the amount of money in the account after time $ t $,
- $ P $ is the principal amount (the initial amount deposited),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time the money is invested for, in years,
- $ e $ is the base of the natural logarithm (approximately 2.71828).

Given:
- $ P = 3000 $ dollars,
- $ r = 5.4\% = 0.054 $,
- $ t = 30 - 18 = 12 $ years.

Now, plug the values into the formula:

\[
A = 3000 \cdot e^{0.054 \cdot 12}
\]

Let's calculate the amount $ A $.The amount in Zeke's account when he is 30 years old will be approximately **$5,735.14**.

Would you like more details on the calculation or have any other questions?

Here are 5 related questions to explore further:

1. How would the amount change if the interest rate was 6% instead of 5.4%?
2. What would be the amount if Zeke had deposited $5,000 instead of $3,000?
3. How much interest will Zeke have earned by the time he is 30?
4. What is the difference in final amount between continuous compounding and annual compounding for the same rate and time?
5. How long would it take for the initial $3,000 to double with the same interest rate?

**Tip:** Continuous compounding generally yields a slightly higher return compared to other compounding methods due to the constant accumulation of interest.

Learn how to calculate the amount in Zeke's account at age 30 with continuous compounding interest. Given an initial deposit of $3,000 at 5.4% interest compounded continuously from age 18 to 30, discover the final amount with detailed step-by-step calculation.

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