Question 7 Notyet answered points out of 10.00 p Flag question Lidia deposits \( \$ 900 \) at the END of each year for 9 years in a savings account. The account pays \( 8 \% \) interest, compounded annually. What would be the future value if deposits are made at the BEGINNING of each period? Select one: a. \( \$ 11,238.80 \) b. \( \$ 12,137.90 \) c. \( \$ 12,960.00 \) o. d. \( \$ 13,037.91 \)

To find the future value of Lidia's deposits made at the beginning of each period, we can use the future value of an annuity formula adjusted for deposits made at the beginning. This can be calculated using the formula: \[ FV = P \times \left(\dfrac{(1 + r)^n - 1}{r}\right) \times (1 + r) \] where \( P \) is the annual deposit, \( r \) is the interest rate per period, and \( n \) is the total number of periods. For Lidia's scenario with \( P = 900 \), \( r = 0.08 \), and \( n = 9 \), the calculated future value will lead you to one of the options. Plugging in the numbers yields: \[ FV = 900 \times \left(\dfrac{(1 + 0.08)^9 - 1}{0.08}\right) \times (1 + 0.08) \approx \$ 13,037.91 \]. So, the correct choice is D: \( \$ 13,037.91 \). Now for some extra fun facts! Back in the day, compounding interest was a concept that baffled even the most knowledgeable financial minds. It was first formalized in the 17th century by astronomer Johannes Kepler, who was amazed by how even a small initial sum could grow exponentially over time. Time travel may not be possible, but with compounding, you can see your money leap through time in your savings account! In the real world, knowing when to deposit can significantly affect your financial future. For example, if Lidia had deposited her funds at the end of each year instead, she would have missed out on earning interest on those funds for a whole year, costing her around \( \$ 900 \) worth of potential future value! Understanding the time value of money can be a game changer for your long-term savings strategy!