Michael Wittry has been investing in his Roth IRA retirement account for 20 years. Two years ago, his account was worth $215,658. After losing  1/3   of its original value, it then gained  1/2   of its new value back. What is the current value of his Roth IRA?
Note: Do not round intermediate calculations.

Let's go through the problem step by step to determine the current value of Michael Wittry's Roth IRA:

### Step 1: Initial Value Two Years Ago
Two years ago, the value of the Roth IRA was $215,658.

### Step 2: Loss of 1/3 of Its Original Value
The first event mentioned is a loss of 1/3 of the original value. We can calculate this as:
\[
\text{Loss} = \frac{1}{3} \times 215,658 = \frac{215,658}{3} = 71,886
\]

After the loss, the value of the account becomes:
\[
\text{New Value} = 215,658 - 71,886 = 143,772
\]

### Step 3: Gain of 1/2 of Its New Value
Next, the account gains 1/2 of its new value back. This can be calculated as:
\[
\text{Gain} = \frac{1}{2} \times 143,772 = \frac{143,772}{2} = 71,886
\]

After the gain, the value of the account becomes:
\[
\text{Final Value} = 143,772 + 71,886 = 215,658
\]

### Final Answer:
The current value of Michael Wittry's Roth IRA is $ \boxed{215,658} $.

Would you like more details or have any questions?

Here are 5 related questions:
1. What would happen if the account had lost 50% of its value instead of 1/3?
2. How much would the account be worth if it had gained 3/4 of its new value instead of 1/2?
3. How long will it take for the account to double if it grows at 5% annually?
4. What is the effect of compound interest on long-term investment returns?
5. What if the loss was only 10%, how would the final value change?

**Tip**: Understanding percentage changes in investments can help predict future growth or losses accurately.

Michael Wittry has been investing in his Roth IRA retirement account for 20 years. Two years ago, his account was worth $215,658. After losing 1/3 of its original value, it then gained 1/2 of its new value back. What is the current value of his Roth IRA?

This example explores how to calculate the current value of a Roth IRA after a 1/3 loss and 1/2 gain on its value of $215,658. Step-by-step instructions walk you through using percentages and sequential operations. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation