annuity due with savings - quan methods self test Q5

Got this question from the self test for quantitative methods in Schweser notes.

Raplh will retire 15 years from today and has saved $121000 in his investment account for retirement.

He beleives he will need 37000 at the beginning of each year for 25 years of retirement with the first date of withdrawal on the first day of retirement.

Ralph expects to earn 8% in his investment account.

the amount he needs to deposit at the beginning of this year and each of the following 14 years (15 deposits in all) is closest to :

either 1350 or 1450 or 1550

PLease help me answer this question, the addition of the 121000 in savings makes the problem difficult for me!!

Hey Leshan:

Firstly try solving from the end and work back-wards… Obviously in BGN mode:

Step 1: FV=0 N=25 PMT=37000 I/Y=8 CPT=PV= - 426564.06

Now you have the FV after the initial 15 years of the investments he needs to make. Because he has saved 121000 already all you need to do is figure out how much he needs to save each year until retirement to reach the 426564.06.

STEP 2: FV=426564.06 N=15 PV=-121000 I/Y=8 CPT=PMT= 1457.2

Answer should be B

When solving for the payment with your calculator, instead of 0 for the present value, you need to put -121,000. I always draw a timeline for this kind of question, it helps a lot!

Amount needed at year 15: N=24, I/Y=8, FV=0, PMT= 37 => PV=389,564 + 37000 = 426,564

Then you can use BGN mode for the second part of the question.

and you solve for N=15, I/Y= 8, PV=-121,000 and FV=426,564 => PMT=1457

If you don’t want to use the BGN mode, you still have some options to find that payment value. For example:

FV at year 14 = 426,564/1.08 = 394,966

PV at year -1 = 121,000/1.08 = 112,037

and solve with N=15, I/Y=8, PV=-112,037, FV= 394,966 => PMT = 1457

Note that you can change the signs of the PV and FV as long as they have opposite signs.

Hope this helps.