Final answer:
To reach a $750 goal in 4 years at a 3% annual interest rate, one would need to invest approximately $666.34 today. However, this calculation does not match any of the answer choices provided, which may indicate an error in the provided choices or the interest rate.
Step-by-step explanation:
The formula for the present value of a single future sum:
To reach a savings goal of $750 in 4 years with an interest rate of 3%, you need to determine how much to invest today using the formula for the present value of a single future sum, which is given by PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the annual interest rate, and n is the number of years. Using the provided values: FV = $750, r = 0.03 (3% as a decimal), and n = 4. Therefore, PV = $750 / (1 + 0.03)^4 = $750 / (1.03)^4. Calculating this gives PV = $750 / 1.1255 = $666.34.
However, none of the options given (A) $698.46, (B) $726.73, (C) $727.69, (D) $731.71 match the calculated amount, suggesting there may be an error in the options provided or the interest rate used. In a real-world scenario, one would need to either use the correct interest rate provided or choose the option that best approximates the calculated value