Final answer:
Keith Bowie should deposit $667.45 into an account today to have enough money in 6 years to pay for the engine overhaul.
Step-by-step explanation:
To determine the amount Keith Bowie should deposit today in an account earning 6% interest compounded annually, we can use the concept of present value. The present value of a future cash flow is calculated by dividing the future cash flow by (1 + interest rate) raised to the power of the number of years. In this case, we want to find the amount needed that would accumulate to cover the engine overhaul cost in 6 years. Let's assume the cost of the overhaul is $390 with a 10% probability, $570 with a 30% probability, $750 with a 50% probability, and $790 with a 10% probability. We can calculate the present value by multiplying each cash flow amount with its respective probability, discounting it back at the interest rate over 6 years, and adding them all up:
Present Value = (390 * 0.10) / (1 + 0.06)6 + (570 * 0.30) / (1 + 0.06)6 + (750 * 0.50) / (1 + 0.06)6 + (790 * 0.10) / (1 + 0.06)6 = $667.45
Therefore, Keith Bowie should deposit $667.45 into the account today to ensure he has enough money on hand in 6 years to pay for the engine overhaul.