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?

Answer 1

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.