This question will require you to apply time value of money methods in a more complex situation. Suppose a grandmother wants to make regular investments to help her new-born granddaughter pay for university. The grandmother is quite sophisticated financially and she wants to save a sufficient amount so that she can pay for the following:

When her granddaughter attends college 18 years from today (luckily she was born on the day when the fall university semester begins), she wants to make the first of 4 annual payments of $25,000 (fees and costs paid on first day of each of the four years of university) to partially pay for her education.

At the date of graduation (which you can assume happens a year after the 4 th payment of $25,000), the grandmother wants to give her graduating granddaughter a gift of $50,000 to use as a deposit on a house.

In order to pay for this plan, the grandmother wants to make 18 equal deposits into an investment account, with the first deposit made on the day of the birth of her granddaughter, the second on the first birthday, and so on, culminating with the eighteenth deposit on the granddaughters 17th birthday.

To be safe, the grandmother will only invest in assets that are expected to pay 5% per year. The timeline for this problem can be drawn as follows:

What annual investments (X) will the grandmother need to make in order to fund this plan? (Hint: Tackle in two steps. First, how much does the grandmother have to save AT t=18, so that 4 subsequent checks of $25K and one of $50K can be paid? Second, how much does the grandmother need to save annually (X), so that the balance at t=18 is the value found in the first part!)

22 P - 17 18 19 20 21 HHHHH -X $25K $25K $25K $25K * $50K