Final Answer:
If Vito has $5,000 per year to invest for 10 years and wants to accumulate $87,745 at the end of that time, he must find an investment that is earning at a rate of 11%. Therefore, the correct option is a. 11%.
Step-by-step explanation:
To calculate the required interest rate for Vito to accumulate $87,745 at the end of 10 years through $5,000 annual investments, the future value of an annuity formula is applied. This formula is FV = P * [(1 + r)^n - 1] / r, where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods.
Substituting the known values: FV = $87,745, P = $5,000, and n = 10 years, we need to solve for the interest rate (r). Rearranging the formula to solve for 'r' involves some complexity due to the presence of exponents and annuity payments. Typically, a financial calculator, spreadsheet software, or financial tables are used to compute this. Using these tools, the interest rate (r) is approximately 11% to achieve the desired future value of $87,745 with Vito's annual $5,000 investments over the specified 10-year period.
Therefore, Vito needs to invest in an option earning an interest rate of approximately 11% annually to accumulate $87,745 by the end of 10 years, assuming he continues to invest $5,000 annually. This calculation aids in understanding the necessary rate of return required for his investment to meet the financial goal within the specified timeframe. Therefore, the correct option is a. 11%.