# CFA Level I - Quant TVM EOC Question | Tricky wording on a Question

“A client plans to send a child to college for four years starting 18 years from now. Having set aside money for tuition, she decides to plan for room and board also. She estimates these costs at \$20,000 per year, payable at the beginning of each year, by the time her child goes to college. If she starts next year and makes 17 payments into a savings account paying 5 percent annually, what annual payments must she make?”

At what time point does the first of the four \$20,000 room and board payments occur?

To break the question statetment down futher:

“A client plans to send a child to college for four years starting 18 years from now."

Drawing a timeline to help us, this means we need to look at Year 18:

``````t16  Year 17  t17  Year 18  t18  Year 19 t19
``````

<—|--------------------|-------------------------|--------------------|—>

Year 18 is flanked by time = 17 (Which marks the beginning of Yeah 18 and end of year 17) & time = 18 (Which marks the end of year 18 and the beginning of the year 19)

The question statement then says: “payable at the beginning of each year”. This means we must select time = 17 as the location of the first investment event, as the phrase “payable at the beginning of each year” always means you have a annuity due.

However, the mark scheme states this question is an ordinary annuity. Can anyone explain to me how this is so and what I did wrong?

The first payment is due right at time t18, i.e. the beginning of the school year.

Thanks for the reply, really appreciate it. Whenever I see the phrase "payable at the beginning of each year " in my mind that instantly tells me i’m dealing with an annuity due.

Couldn’t they have equally said "The annuity starts 19 years from now, payable at the beginning of each year" to show it is indexed at the beginning of year 19 (Time = 18)?

Cheers

Let’s say Little Suzie is born 1 September 2023. Exactly 18 years later, she is off to start college (1 September 2041), At that time, the college will expect the \$20K room and board. They could have also said end of the year (1 September 2042) to imply an immediate annuity.

If you see phrasing “that starts x years from now”, assume the cash flow happens at exactly time x. And yes, if you see “beginning of the year/month/etc”, “now”,“today”, the question writer is usually hinting to treat the problem as an annuity due.