Theba and Marek have been married for nearly $20$ years. They are both $45$ years of age and have two children in high school. They are concerned about how to fund their future retirement costs, as well as how to help their children pay for college.

Instructions

Answer the following questions.

a$.$ Assume that Theba and Marek have a combined annual income of $$95,000.$ Also assume that they want to retire at age $67.$ If inflation$$or the annual cost of living$$increases by $3\%$ per year, how much income will they need in retirement to maintain their current standard of living?

b$.$ Marek is interested in purchasing a second home overlooking a mountain lake. He believes that they should buy this home soon, make payments while they are working, use it for vacations, and move into the house permanently once they retire. If they need a down payment of $$35,000,$ how much should they save annually over the next $7$ years? Assume that they can earn $7\%$ on their annual savings.

c$.$ Their daughter, Chyna, is interested in attending a prestigious college. The annual tuition, plus room and board and other fees, is about $$65,000$ per year. College costs are increasing at a $5\%$ rate per year. The college typically awards to applicants with a household income of $$95,000$ scholarships and grants equal to $70\%$ of the total cost of college. Help Theba and Marek determine how much college will cost, based on this information and assuming that Chyna is $15$ years of age and will start college at age $18.$

$1.$ What will be the total cost of college when Chyna starts?

$2.$How much will Theba and Marek need to pay when Chyna starts college?

$3.$Based on your answer, how much will they need to save per year starting today to fund one year$$s worth of net college expenses if they can earn $7\%$ APY on their savings?