Final answer:
To reach a savings goal of $4,863 with monthly deposits of $145 and a 7% interest rate, financial tools must be used to solve for the time, as there is no straight algebraic approach. Starting to save early and taking advantage of compound interest is essential for financial growth.
Step-by-step explanation:
To calculate the time required to save $4,863 with monthly deposits of $145 at a 7% annual interest rate, we need to use the future value of an annuity formula. Unfortunately, there is no simple algebraic solution to this problem because it involves solving for the time component in the compound interest formula. However, financial calculators and spreadsheet programs can be used to determine the period.
To find the length of time needed, we can iterate different time periods in the formula until we reach the future value close to $4,863. Alternatively, using a financial calculator or software with a built-in function for the future value of an annuity could provide a more efficiently.
The principle of compound interest greatly impacts the time it takes to reach a savings goal. Starting early and consistently investing can yield substantial growth over time, as demonstrated by the given example of a $3,000 investment growing to $44,923 in 40 years with a 7% return. To reach your goal for your anniversary, based on the information provided, professional financial tools or advice may assist in determining the exact period required.