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 of its original value, it then gained of its new value back. What is the current value of his Roth IRA?
Let's assume the original value of Michael's Roth IRA retirement account was x.
After 20 years, the account value becomes x * (1 + 0.05)^20 = x * 1.0512^20.
We are given that x * 1.0512^20 = $215,658.
So, x = $215,658 / 1.0512^20.
Two years ago, the value of the account was x * (1 - 0.75).
So, x * (1 - 0.75) = (215658 / 1.0512^20) * (1 - 0.75).
The account has then gained 0.75 of its new value back, so the current value of the account is (215658 / 1.0512^20) * (1 - 0.75) * (1 + 0.75).
Calculating this equation, the current value of Michael's Roth IRA is $215,658.
To determine the current value of Michael Wittry's Roth IRA, we need to calculate the gain and add it to the original value.
1. Calculate the gain:
- Michael's account lost 50% of its original value.
- It then gained back 50% of its new value.
- Total gain = (50% loss) + (50% gain after loss) = 0% gain/loss.
2. Add the gain to the original value:
- Original value = $215,658.
- Gain = $215,658 * 0% = $0.
Therefore, the current value of Michael Wittry's Roth IRA is $215,658.