Effective annual rate

CFA Level I Quant
#1

A $100000 CD, quarterly compounded, will return $123528 in two years. What is the effective and stated annual rates for this.

Please reply.

#2

I think the question isn’t complete. Using the TVM worksheet, I got 10.71% as I/Y. That was the most I could do with the available information.

#3

(123,528 / 100,000) - 1 = 23,53% (effective yield for 2 years) (23,53 / 100)+1)^0,5) - 1) * 100 =11,14% (effective yield for 1 year)

Using the ICONV Worksheet with EFF = 11,14% and C/Y = 4 gives a NOM of 10,71%. This is the nominal annual yield. Regards, Oscar

#4

To get the quarterly rate: 123528/100000 = 1.2353 -> 1.2353^0.125 = 1.0268.

To get the stated annual rate: 0.0268*4 = 0.1072 = 10.72%

To get the effective annual rate: 1.0268^4 - 1 = 1.1116 - 1 = 0.1116 = 11.16%

#5

This is essentially what I did to solve.

#6

I want to know where I can get a CD paying about 11% per year.

#7

If you have time to do the algebra by hand, then by all means go for it. Also, keep in mind that your calculator has some wonderful pre-programmed functionality in it: let TVM, ICONV, or even IRR do all that drudge arithmetic and iterating.

#8

How do you use the ICONV function?

#9

This is how it works on the TI BA II Plus Professional:

2nd --> ICONV --> Enter either NOM for the nominal rate or EFF for the effective rate and C/Y for the number of compunding periods p.a. Then switch to either NOM or EFF and press CPT to compute the rate you are looking for.

Best,

Oscar

#10

Thanks Oscar!