2. How much was deposited in Emily’s account if it grew to $7,626 with
a 4.2% interest rate, compounded monthly, after 6 years and 9
months? (Hint: For t, don’t just put in 6. Put in a value for t that
represents 6 years, 9 months as a decimal. In other words, what is “9
months” as a decimal?) 

We can solve this problem using the formula for compound interest:

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

Where:
- $A$ is the final amount ($7,626 in this case),
- $P$ is the initial deposit (what we are solving for),
- $r$ is the annual interest rate (4.2%, or 0.042 as a decimal),
- $n$ is the number of times the interest is compounded per year (monthly, so $n = 12$),
- $t$ is the time in years.

### Step 1: Convert the time
6 years and 9 months = 6 years + $\frac{9}{12}$ = 6.75 years. So $t = 6.75$.

### Step 2: Rearrange the formula to solve for $P$:
\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]

### Step 3: Plug in the values:
- $A = 7,626$,
- $r = 0.042$,
- $n = 12$,
- $t = 6.75$.

Now let's calculate the initial deposit $P$.The initial deposit that Emily made was approximately **$5,746.31**.

Would you like any further details or explanations on this?

Here are 5 related questions to explore:
1. How would the deposit change if the interest rate was 5% instead of 4.2%?
2. What if the interest was compounded quarterly instead of monthly?
3. How long would it take for the deposit to double at the same interest rate and compounding frequency?
4. How would the final amount change if the deposit was $6,000 instead of $5,746.31?
5. What would the initial deposit be if the interest rate was 3.5%, compounded monthly?

**Tip:** When dealing with time in financial problems, always convert the time period into a decimal to ensure accurate results.

How much was deposited in Emily’s account if it grew to $7,626 with a 4.2% interest rate, compounded monthly, after 6 years and 9 months? (Hint: For t, don’t just put in 6. Put in a value for t that represents 6 years, 9 months as a decimal. In other words, what is “9 months” as a decimal?)

Discover how to calculate the initial deposit in a compound interest scenario where the account grows to $7,626 at a 4.2% annual interest rate, compounded monthly, over 6 years and 9 months. This problem includes converting time to decimal and applying the compound interest formula. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation