# medium level - quant

what is the FV of four semiannual payments given a int rate of 10% compounded quarterly. a) 430.11 b) 430.71 c) 431. 12 e) 431.41

I tried it and got 431.41

We need to sum up the FV of the single 4 payment at 10%.

Assuming 100 is the semianual payment after 1st 6 months you have - 100 AFter 1yer = 100 * (1.025)^2 = 105.0625 Your amount starting of second year = 100 + 105.0625 = 205.0625 After 18 months you have 205.0625 * (1.025)^2 = 215.443 Your amount starting of last 6 month period = 100 + 215.443 = 315.443 Your value without last payment at 2 years = 315.443 * (1.025)^2 = 331.4131 Adding last 100, FV = 331.4131 +100 = 431.4131. Is d (e ?) the answer ?

oops, the question was missing semiannual payments of \$100 and the answer is e

did you make this up? I t is poorly worded

You need to figure out the semiannual rate from teh quarterly rate, then plug in. [1+(x/2)^2]-1=10.38% where 10.38% is the efective annual rate based on quarterly-compunding. Solve for x, you get x=10.125% (annual rate based on semi-compunding. Divide that by 2, and use as your interest rate to compute 4 semi-annual payments future value. E is correct.

No need for the \$100.

How can the todays fair value be above 400 \$?

question is asking for FV and dreary, alternatively you could do, (1 + .025)^2 - 1 to get your effective Semiannual rate. that way you first dont have to compute effective annual rate.

yes, this is more straightforward.

pepp Wrote: ------------------------------------------------------- > what is the FV of four semiannual payments given a > int rate of 10% compounded quarterly. > > a) 430.11 > b) 430.71 > c) 431. 12 > e) 431.41 I finally got it. You do first EAR = ( 1 + PIR) ^ N - 1 to get real rate by which you discount this annuity I did EAR = ( 1 + 10%/4)^2 - 1 EAR = (1 + 2.5%)^ 2 - 1 = 5.063% then, do a FV of an annuity with these inputs PMT = (100) n = 4 i = 5.063% FV = … \$431 dunk shot

is fv =final value or fair value?

FV = FUTURE VALUE look at your calculator!!!

I/Y = 1.025^2 - 1 = 5.0625% N= 4 PMT = 100 (my feeling tells me it’s either 100 or 1000) PV = 0 CPT FV = 431.41

heha168 Wrote: ------------------------------------------------------- > I/Y = 1.025^2 - 1 = 5.0625% > N= 4 > PMT = 100 (my feeling tells me it’s either 100 or > 1000) > PV = 0 > CPT FV = 431.41 ************* PMT difference (100 or 1000) shouldnt matter too much. CFAI is testing us to see how quick we can assemble and dissect this problem into its 2 pieces.

thanks daj.

Dreary Wrote: ------------------------------------------------------- > You need to figure out the semiannual rate from > teh quarterly rate, then plug in. > > [1+(x/2)^2]-1=10.38% > where 10.38% is the efective annual rate based on > quarterly-compunding. > Solve for x, you get x=10.125% (annual rate based > on semi-compunding. > > Divide that by 2, and use as your interest rate to > compute 4 semi-annual payments future value. > > E is correct. Dreary, Your solution is very clear but you said “no need for the \$100”? Where does \$100 come from or is it understood by default?

> > Your solution is very clear but you said “no need > for the \$100”? Where does \$100 come from or is it > understood by default? understood by default. This was new to me, too

You all know about the iconv button right? To get EAY? Just checking.