# Quantitative question

I apologize if it has already been solved but I can’t seem to find it using the search feature. an investor is celebrating his 50th birthday 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 birthday for 20 years following his retirement, with the first withdrawl being made on his 66th birthday. After extensive reserach the investor determines that he can deposit his money into an account that offers 5% interest per year (compounded quarterly). He wants to make equal annual payments on each birthday into the account–the first payment on his 51st birthday, and the last on his 65th birthday. 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 birthday to enable him to make the desired withdrawls at retirement? A. 7,305 B 9,411 C 12,667 D 15,549

The question can be broken into three parts: (1) how much does the investor need on his 65th birthday, (2) how much is his employer contributing, (3) what annual payments need to be made for 15 years to get a future value equal to (2) - (1). (1) N = 20, i = 5.0945337% (this is the effective annual rate given quarterly compounding), FV = 0, PMT = -15,000. Solve for PV to get \$185,443.83. This is how much he needs on his 65th birthday. (2) N = 180, i = 5.0945337/12 = 0.4245445%, PMT = 100, FV = \$26,940.94. This is how much his employer is contributing to the amount he needs on his 65th birthday. So the investor needs \$185,443.83 - \$26,940.94 = \$158,502.89 on his 65th birthday. (3) N = 15, i = 5.0945337%, FV = \$158,502.89, PV = 0 Solve for PMT to get \$7,293.28. I believe the approximately \$12 difference from answer A is rounding.

You`ll never get a question like that in the exam. Its too long. Focus on the just the short questions. The long ones are just a waste of time.

that’s bad advice. The above can easily be solved in 1.5 minutes with a calculator if you know the concept.

you really managed to read and answer it in 1.5min? I re-read that paragraph 3 times and still didnt understand the question. Doomed.

thanks for the help cheb…i got it now

I agree that the problem is too long for the exam. It’s a good practice problem though.

it seems like the questions on the CFA I exams are much shorter than the ones from book 6 on schweser online.