Last year, Ivanna opened an investment account with 

$8400

. At the end of the year, the amount in the account had increased by 

29%

.

(a)

Fill in the blank to write the year-end amount in terms of the original amount. Write your answer as a decimal.

Year-end=amount×Originalamount

(b)

Use your answer in part (a) to determine the year-end amount in Ivanna's account.

Year-endamount:$


### Part (a): Writing the year-end amount in terms of the original amount

To express the year-end amount in terms of the original amount, we need to account for the 29% increase. The formula will be:

\[
\text{Year-end amount} = (1 + \text{percentage increase}) \times \text{Original amount}
\]

Since the percentage increase is 29%, we convert it to decimal form:

\[
29\% = 0.29
\]

So, the expression becomes:

\[
\text{Year-end amount} = (1 + 0.29) \times \text{Original amount} = 1.29 \times \text{Original amount}
\]

### Part (b): Determining the year-end amount in Ivanna's account

Now, using the formula from part (a), we can calculate the year-end amount. The original amount is $8400, so we substitute that into the formula:

\[
\text{Year-end amount} = 1.29 \times 8400
\]

Let's calculate the result.The year-end amount in Ivanna's account is $10,836.

### Summary:
- **(a)** The year-end amount is expressed as $ 1.29 \times \text{Original amount} $.
- **(b)** The year-end amount in Ivanna's account is $10,836.

Do you have any questions or need further details?

Here are 5 related questions to expand your understanding:
1. How would the result change if the percentage increase was 15% instead of 29%?
2. What would be the year-end amount if Ivanna started with $5000 instead of $8400?
3. How would you calculate the percentage increase if you only knew the year-end and original amounts?
4. If Ivanna's account grows by 29% again next year, what would the total amount be after two years?
5. What formula would you use to calculate the year-end amount if the percentage increase changed every year?

**Tip:** When calculating percentage increases, converting the percentage to a decimal (by dividing by 100) ensures accurate results.

Last year, Ivanna opened an investment account with $8400. At the end of the year, the amount in the account had increased by 29%. (a) Fill in the blank to write the year-end amount in terms of the original amount. Write your answer as a decimal. Year-end = amount × Original amount. (b) Use your answer in part (a) to determine the year-end amount in Ivanna's account.

Learn how to calculate the year-end investment amount with a 29% increase for an initial investment of $8400. This problem involves percentage increases and multiplication with decimals, making it suitable for students in Grades 6-8.

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