You begin planning for a down payment on a home. You want to buy a home in 8 years, and you'd like to earn at least \( \$ 20,000 \) in interest. You find an investment that will pay \( 5 \% \) simple interest each year. How much principal must you invest to meet your goal? a.) \( \$ 60,000 \) b.) \( \$ 50,000 \) c.) \( \$ 8,000 \) d.) \( \$ 5,000 \)

To calculate the principal needed to earn at least \( \$ 20,000 \) in interest over 8 years at a \( 5\% \) simple interest rate, you can use the formula for simple interest: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] Rearranging this gives: \[ \text{Principal} = \frac{\text{Interest}}{\text{Rate} \times \text{Time}} = \frac{20000}{0.05 \times 8} = \frac{20000}{0.4} = 50000. \] Therefore, the principal must be \( \$ 50,000 \), which is option b.) Investing in the right vehicle can significantly impact your savings. If you consistently contribute a portion of your income to reach your down payment goal, you'll not only benefit from interest but also build a strong habit of saving. Consider automating your deposits into a savings account or an investment fund; this way, you're less tempted to spend it and more likely to see your wealth grow! Also, don't forget to account for inflation during your planning. Over 8 years, the purchasing power of your money may decrease. This means that your \( \$ 20,000 \) may not stretch as far in the future. Always keep an eye on the market trends and consider diversifying your investments to maximize potential returns over time!