# Quant Qs -Tough

Quant Q from Exam 3 Am sure this Q must have come up on this forum. Please help. An investor is celebrating his 50th b/day today and wants to start saving for his anticipated retirement at age 65. He wants to be able to withdraw \$15,000 from his savings account on each b/day for 20yrs following his retirement, with the first withdrawal being made on his 66th b/day. After extensive research, the investor determines that he can deposit his money into an account that offers 5% interest per yr (compounded quarterly). He wants to make equal annual payments on each b/day into the account-the first payment on his 51st b/day, and the last on his 65th b/day. In addition, the investor’s employer will contribute \$100 to the account at the end of every month as part of the company’s profit sharing plan ( a total of 180 contributions). What amount must the investor deposit personally each year on his b/day to enable him make the desired withdrawals at retirement? a. \$7 305 b. \$9 411 c. \$12 667 d. \$15 549 Q 2 An analyst develops the following information for two stocks. 50% of the funds are invested ineach stock. Scenario 1 Scenario 2 Scenario 3 Probability 0.5 0.3 0.2 Rate of Return Stock A 25% 10% -25% Stock B 1% -5% 35% The expected return and the variance of this two stock protfolio are closest to: Expected Return Variance a.8.25% 23.31% b. 8.25% 48.09% c.10.5% 23.31% d.10.5% 48.09% Thanks for your help.

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i got (A) for 1st.

Q2 It turns out that 23.31% = 48.09% ^ 2 so you may guess 23.31% for variance.

smartrisk for Q1 you got it but how did u arrive at the answer, i solved if for hrs but cudnt and I gave up thats why i floated it here becos i also met a similar Q in another paper and thought it was surely testable material would greatly appreciate your few but very expensive minutes at this pt in time good luck in your exams

Firstly convert that 5% compounded quarterly into yearly ==> (1+0.25)^2-1= 5.09 Get the target amount: 15000 for 20 years PMT=15000, N=20, I/Y=5.09, FV=0, CPT -> PY= 185,514.84 Get the employers contribution till the end of 65thBday: I/Y=5.09/12 =0.4242, PMT=100, PV=0, N=180, CPT --> FV=26930.72 So the actual target amount =185,514.84- 26930.72= 158584.12 Now find out how much to invest per year: N=15, I/Y=5.09, PV=0, FV= , CPT-> PMT=7299.51 Hope this helps. Also, All calculations are done in END mode ( i don’t really change the mode anyway). The last thing I want is to mess up other questions too.

Sorry, I made a typo with the initial rate compounding, Its (1.0125)^4-1=5.09

smartrisk many thanks good luck in your exam

Does anyone have an explanation for #2?

# 2 you just need to calculate probability weighted return and then prob weighted covariance then plug into the variance of a portfolio formula. it’s not hard but its time consuming.

I am aware. I have tried it though and it does not seem to work. Expected value is 8.25% When I try to calc variance, it doesn’t seem to compute to any of the options. Can someone confirm that it works?

variance of portfolio = (0.5 * ((13-8.25)^2)) + (0.3 * ((2.5-8.25)^2)) + (0.2 * ((5-8.25)^2)) = 23.3125 I put in the () where I type them into my calculator but, when I took the test, I used actuaryalfred’s method to save time (then went back to actually calculate it when I had extra time left after finishing the questions)

Thx I see my mistake now

if i see one of those long tvm questions that have to do with college tuition, retirement, etc. im skipping it and going back to it at the very end only if theres time. it takes up a largely disproportionate amount of time, plus ill prob get it wrong anyway

Newsuper was just wondering how one would ‘search’ where Qs and non standardised discussions are posted on a forum like this. please share the skills with me, it will help me later regards