Hardest quant question EVER

I was feeling comfortable about Quant until this question appeared on my mock. It was the very first quant question and completely threw me off my game for the rest of the exam. This question took up half the page.

A client is celebrating his 50th b-day and wants to start saving for his anticipated retirement at age 65. he wants to be able to withdraw $20,000 from his saving account on his 66th b-day and each year for 19 more years after that.

After extensive research, the client determines that he can invest his money in an account that offers 5% interest per year with quarterly compounding. he wants to make equal annual payments on each b-day into the account - the first payment on his 51st b-day and his last on his 65th b-day.

In addition, the clients employer will contribue $2000 to the account each year (beginning on the clients 51st b-day) as part of the companies profit-sharing plan (a total of 15 contributions.)

The amount the client must deposit personally into the account each year on his b-day to enable him to make the desired wds at the retirement is closest to:

A. 9375


C. 11400

Ok, so with this question, i know this is where you use n = one previous. Also, the 3rd paragraph really threw me off. Where a seperate amount is also contributed to the account… Can someone please share with me your approach/mind set for this question?


First, we need to know how much he needs in his account on his 65th birthday.

Annual effective rate = (1.0125)^4 – 1 = 5.0945%

FV = 0

n = 20

PMT = 20,000

Solve for PV = -247,259

Now, calculate the required (total) payment:

n = 15

i = 5.0945%

PV = 0

FV = 247,259

Solve for PMT = $11,377

Client’s contribution = $11,377 – $2,000 = $9,377.

Answer: A) 9375.

you are really magician…

It would help to do a timeline in this type of question to break it down and better understand the scenario