Marcus receives an inheritance of ​$2,000. He decides to invest this money in a 12 year certificate of deposit​ (CD) that pays 4.5​% interest compounded monthly. How much money will Marcus receive when he redeems the CD at the end of the 12​ years?

To find out how much money Marcus will receive when he redeems the CD at the end of 12 years, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money accumulated after $ n $ years, including interest,
- $ P $ is the principal amount (the initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times that interest is compounded per year,
- $ t $ is the time the money is invested for in years.

**Step 1: Identify the known values.**
- Principal ($ P $): $2,000
- Annual interest rate ($ r $): 4.5% or 0.045
- Number of times interest is compounded per year ($ n $): 12 (since it is compounded monthly)
- Time ($ t $): 12 years

**Step 2: Plug the values into the compound interest formula.**

\[
A = 2000 \left(1 + \frac{0.045}{12}\right)^{12 \times 12}
\]

**Step 3: Simplify and calculate.**

\[
A = 2000 \left(1 + \frac{0.045}{12}\right)^{144}
\]
\[
A = 2000 \left(1 + 0.00375\right)^{144}
\]
\[
A = 2000 \left(1.00375\right)^{144}
\]
\[
A \approx 2000 \times 1.7137
\]
\[
A \approx 3427.48
\]

So, Marcus will receive approximately **$3,427.48** when he redeems the CD at the end of the 12 years.

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions:
1. What would be the amount if the interest was compounded quarterly instead of monthly?
2. How much would Marcus receive if the interest rate was 5% instead of 4.5%?
3. What is the difference between simple and compound interest for the same scenario?
4. How would the final amount change if the investment period was 10 years instead of 12?
5. How does the frequency of compounding (monthly, quarterly, annually) affect the final amount?

**Tip:** When dealing with compound interest, the more frequently the interest is compounded, the higher the final amount will be.

Learn how to calculate compound interest with monthly compounding for Marcus's investment of $2,000 in a 12-year CD at 4.5% interest. Get a detailed step-by-step solution with formulas and calculations. Suitable for high school students and anyone interested in finance and investments.

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