Questions: Mark wants to have enough money invested in his retirement portfolio so that he can earn 30,000 interest each year. If the portfolio pays 8.2% simple interest, how much will he need to have invested in the portfolio?

Solution Steps

To find out how much Mark needs to invest, we can use the formula for simple interest: \( I = P \times r \), where \( I \) is the interest earned, \( P \) is the principal amount (the amount invested), and \( r \) is the interest rate. We need to solve for \( P \) given that \( I = 30,000 \) and \( r = 8.2\% \) (or 0.082 as a decimal).

We are given:

• Desired interest \( I = 30000 \)
• Interest rate \( r = 0.082 \)

The formula for simple interest is given by: \[ I = P \times r \] To find the principal amount \( P \), we rearrange the formula: \[ P = \frac{I}{r} \]

Substituting the known values into the equation: \[ P = \frac{30000}{0.082} \]

Calculating the value gives: \[ P \approx 365853.6585 \]

Final Answer