Annuity Due?

[PsychMeister]

Hi,
Got this problem from the 2016 CFAI book volume 1 practice test in Quantitative basics. I’m leaving the rest out as this is the only part that confuses me:
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 $20,000 per year, payable at the beginning of each year, by the time her child goes to college. Interest is at 5%.
So, noticing the bolded text (it’s not bold in the textbook), I computed for the PV at t=18 and set my calculator to BGN. But, the answer being given by the textbook states otherwise. Why is that?
My calc:
N: 4
I/Y: 5
PMT: 20,000
Result PV: 74,464
Textbook Answer:
N: 4
I/Y: 5
PMT: 20,000,
Result PV: 70,919

 

[moxnguyen]

I think It is payable at the beginning of the year => have not paid, therefore, not a Cash flow at the beginning of the year.
Well, i think it is so tricky here

 

[Moonborne]

You first steps are correct, you set the calculator to BGN mode, put in 4 payments of $20,000 at 5% interest rate, which results in the PV at t = 18. Now the question also states that the client will make 17 payments starting at t = 1 to reach the computed PV. This means that we have to discount $74,646 one more year to derive $70,919 at t = 17. This will be the future value. The last payment will be at t = 17, it will earn interest 1 year at 5%, we arrive at t = 18 and the child starts college with the first payment of $20,000.
1. BGN mode, N = 4, i = 5, PMT = -20000, CPT PV = $74465. (PV at t = 18).
2. 74465 / 1.05 = $70919 (PV at t = 17).
3. END mode, N = 17, i = 5, FV = 70919, CPT PMT = -$2744.50 (correct answer).
Alternatively, you could have performed step 1 in END mode and calculate the PV at $70919 immediately, skipping step 2. Why does that work? Because the PV computed in END mode is the PV one period prior to the first payment (t = 17), whilst in BGN mode the PV is calculated at the first payment (t = 18).

 

[PsychMeister]

Thank you, Moonbone. I think I get it now. So, basically, I should have correlated the payments to how much the savings would be by end of T=17. If the 17 payments were not in the problem, the parameters I have used would have been correct.

 

[Moonborne]

The difference here with a ‘simple’ problem is the 17 payments in 18 years, instead of 18 payments in 18 years. If the question stated the client makes 18 saving deposits until t = 18 where the first college tuition payment is made, you would set to BGN mode, calculate the $74465. Set to END mode, use that as FV and calculate yearly saving deposit. The oddity here is that the final saving deposit is made at t = 17, the entire value of the savings account accrues 1 year of interest without any saving deposit until t = 18.