Quant-Time value of Money

CFA Level I Quant
#1

Hi,

I found this question online and but don’t know the answer. Could someone please advise if I have correctly done calculated? I am practicing time value questions to master them as were getting them wrong initially.

Q: Paul Hauser deposits $15,000 on Jan 1st and Jul 1st every year for 8 years. The account pays an interest rate of 5.2% per year, compounding quarterly. At the end of the eighth year, Hauser’s deposit is closest to:
A) $299,700
B) $300,600
C) $301,100

I put the calculator at the “beginning mode” and used the values: PV=0, Pmt= -$15,000, I/Y= 2.6, N=16 and getting an answer of “B” $300,600. Is it correct?

#2

Ay mijo. :frowning_face: :broken_heart:

Try setting P/Y=2, C/Y=4 and I=5.2.

#3

Because the deposits are made semiannually, you need to use the effective semiannual rate, which is:

(1 + 5.2%/4)2 – 1 = 1.0132 – 1 = 2.6169%

#4

I have BA plus calculator, can’t use C/Y. It should be I/Y. Any thoughts?

#5

Thank you. I used 2.6169% with the beginning mode and get the answer $301,055. None of the above choices has this answer.

#6

Note that the question asks you which answer is closest to the correct answer.

If you round $301,055 to the nearest $100, you get answer C.

#7

2nd I/Y gets you to the P/Y and C/Y settings. :nerd_face:

#8

sounds good, thanks millions.

#9

Thanks very much for your response and help. I tried with P/Y and C/Y settings but not getting any of the answers, but I understood the concept explained above by magician.

#10

Using P/Y=2 , C/Y=4 and BEG

16 N 5.2 I PMT 15,000 CPT FV -301,055.5726

Using P/Y =1 C/Y = 1 and BEG

16 N 2.6169 I (see s2000magician’s explanation above) 15,000 PMT CPT FV -301,055.5726

Closest answer is C. :blush:

#11

thanks so much, I appreciated the clarification and I learnt a new/different way of solving the problem. Have a great day!

#12

The correct answer should be C.
If we don’t use the financial calculator, we can try solve the problem like this, in order to simplify the calculation, first, we can transform the quarterly-compounded to continuously compounded, the calculation are listed as follows:
(1+0.052/4)^4=e^x.
So x=0.051664901
Next we compounded the cash flow to the end of the eighth year:
15000(e^8x+e^7.5x+e^7x+…+e^0.5x)=301055.5726

If you use the financial calculator, mine is BA2 plus:
We pay cash flow 2 times in a year, compounded quarterly, so
P/Y=2 C/Y=4 then N=16 I/Y=5.2 PV=0 PMT=15000 FV=-301055.5726
Also, you can compounded semiannually, than
P/Y=2 C/Y=2 then N=16 I/Y=5.2338 PV=0 PMT=15000 FV=-301055.5726
All with BGN mode. (Press 2nd PMT, if the screen shows end, than press 2nd enter to activate BGN)