Tamara invested ​$15,000 in a money market account with an interest rate of 1.25​% compounded semiannually. Three years​ later, Tamara withdrew the full amount to put toward the down payment on a new house. How much did Tamara withdraw from the​ account?

To determine how much Tamara withdrew from her account, we need to use the formula for compound interest:

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

Where:
- $ A $ is the final amount (the amount withdrawn),
- $ P $ is the principal (the initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years the money is invested.

### Given:
- $ P = 15,000 $,
- $ r = 1.25\% = 0.0125 $,
- $ n = 2 $ (since interest is compounded semiannually),
- $ t = 3 $ years.

Now, we can calculate:

\[
A = 15,000 \left(1 + \frac{0.0125}{2}\right)^{2 \times 3}
\]

\[
A = 15,000 \left(1 + 0.00625\right)^{6}
\]

\[
A = 15,000 \left(1.00625\right)^{6}
\]

Let me calculate this for you.After 3 years, Tamara withdrew approximately **$15,571.36** from her account.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What if the interest rate had been compounded quarterly instead of semiannually?
2. How would the final amount change if Tamara had invested for 5 years instead of 3 years?
3. How does the frequency of compounding affect the final amount?
4. What if the interest rate was 2% instead of 1.25%—how much would she withdraw?
5. How can we calculate the interest earned over the 3-year period?

**Tip:** The more frequent the compounding, the greater the interest accumulation over time.

Tamara invested ​$15,000 in a money market account with an interest rate of 1.25% compounded semiannually. Three years​ later, Tamara withdrew the full amount to put toward the down payment on a new house. How much did Tamara withdraw from the​ account?

Discover how to calculate the amount Tamara withdrew after investing $15,000 in a money market account with a 1.25% interest rate compounded semiannually for 3 years. This step-by-step solution highlights key concepts in compound interest and exponential growth, suitable for Grades 9-12.

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