With Interest and TVM Compute the amount of money to be set aside today to ensure a future value of \( \$ 3,000 \) in one year if the interest rate is \( 5.5 \% \) annually, compounded annually. The amount of money to be set aside is \( \$ \square \). (Round to the nearest cent as needed.)

To calculate the present value (PV) required to achieve a future value (FV) of \( \$3,000 \) in one year at an interest rate of \( 5.5\% \), you can use the formula: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \( FV = 3000 \) - \( r = 0.055 \) - \( n = 1 \) Plugging the values in: \[ PV = \frac{3000}{(1 + 0.055)^1} = \frac{3000}{1.055} \approx 2845.88 \] So, to ensure that you have \( \$3,000 \) in one year, you need to set aside approximately \( \$2,845.88 \). Here’s an interesting tidbit: the concept of time value of money (TVM) is crucial in finance because it helps people understand how to effectively manage their money over time. The idea is that money available today is worth more than the same amount in the future due to its potential earning capacity, like earning interest! In real life, knowing how to calculate present and future values can be extremely beneficial for financial planning. Whether you're saving for a vacation, retirement, or a major purchase, understanding how to use interest rates and the concept of compounding can help you strategize the best way to grow your savings or budget effectively.