Reading 6 TVM: Practice Question 15 from Curriculum

CFA Level I Quant
#1
  1. For a lump sum investment of $250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to $1000,000 is closest to -

A. 555

B. 563

C. 576

The calculation in answer section seems to be difficult. Why they calculated Effective Annual Rate first? Even use of Ln and shown answer is inconsistent. Would you please give me a fresh solution?

Thanks in Advance.

#2

Using daily compounding:

250,000 * (1 + 0.03/365) ^ n = 1,000,000

(1 + 0.03/365) ^n = 4.0

n * ln (1+0.03/365) = ln 4.0

n = ln 4.0 / ln (1 +0.03/365)

n = 16,867.27 days

n = (16,867.27/365) * 12 months = 554.54 months

Using EAR of 3.0453%

250,000 * (1 + 0.030453) ^ n = 1,000,000

(1 .030453) ^n = 4.0

n * ln (1.030453) = ln 4.0

n = ln 4.0 / ln (1.030453)

n = 46.21171 years

n = (12*46.21171) months = 554.54 months

#3

Hello Pantho,

Using BA II Plus Pro: all keys will be represented as follow : (name of the key).

  1. Clear

  2. Set (C/Y) to 365

  3. Compute for a standard unknown period with (PV) = -250,000 ; (FV) = 1,000,000 ; (I/Y) = 3.

  4. You should get (N) = 46.21171

  5. Time by 12 and that is 554.54

Done in 30s :slight_smile:

Regards

#4

even better

do not set P/Y or C/Y on your calculator ever

I/Y=3/365

PV=-250000

FV=1000000

CPT N -> 16827

16827 / 365 * 12 --> 553.216 months

I would recommend not to set up C/Y or P/Y in your computations - because you could end up messing future calculations.

#5

:broken_heart: :-1:

I set P/Y and C/Y as given in the problem and let the calculator do the grunt calculation. Sure, the stated problem here has a single payment at time 0 and daily compounding, but then you get the nastier situations, such as annuities where P/Y<>C/Y and each is some wonky value.

#6

BreadMaker

You may not agree with my approach. The reason for my doing so, is just a safety mechanism.

Whatever you set C/Y or P/Y numbers too - carry on for all future calculations.

They also do not clear if you do 2nd Clr TVM on the calculator.

Hence could result in weird wonky answers on future calculations …

(if the test setter recognizes this - one of the possible answers could be accounting for this mistake - and you would get a question wrong).

Hence this advice - - there are other ways - which is to set the I/Y to value divided by the # of P/Y e.g. as I did above in my set up

I/Y=3/365

#7

It’s all good. Different strokes for different folks.