Forums › Ask ACCA Tutor Forums › Ask the Tutor ACCA MA – FIA FMA › Annual effective interest rate

- This topic has 8 replies, 2 voices, and was last updated 9 years ago by John Moffat.

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- November 12, 2014 at 5:31 pm #209422
an investor has the choice between two investment . investment exe offers interest of 4% per year compounded semi annually for a period of 3 years. investment wye offers one interest payment of 20% at the end of its 4 year life . what is the annual effective interest rate offered for the two investments ?

sir please answer me this question .

Thank you !!!November 12, 2014 at 6:21 pm #209447Exe gives 2% (4%/2) every six months.

If you invested 100, then after six months it would be 102. After another 6 months it would be 102 x 1.02 = 1.0404. This is the same as 4.04% per year.

If Wye was giving interest of R every year, then 100 invested for 4 years would grow to 100 x (1 + R)^4.

So 100 x (1+R)^4 must equal 100 x 1.20

So 1+ r = the fourth root of 1.20

November 12, 2014 at 6:48 pm #209469sir how you calculated wye interest i didnt get it . can you try another method ?

November 12, 2014 at 6:58 pm #209473There is no other method!

To add on 20% at the end of 4 years you multiply by 1.20

To add on interest of r every year you multiply by (1+r)^4

(Have you watched the free lectures on interest?)

November 12, 2014 at 7:24 pm #209482sir,but from where you got 1.20 ???

yes offcourse i watched all the lecturessir,

1+R = (1+.05)^4 can we do in like this method something like this ???November 12, 2014 at 7:56 pm #209485sir in the answer back of text given like :

1.20^0.25-1= 0.0466 or 4.66%

sir forget about all the above question ii asked . sir just say me how they got

0.25 ?November 13, 2014 at 9:41 am #209544I wrote that if r is the annual rate, then (1+r)^4 = 1.20

Therefore (1+r) = fourth root of 1.20

From your school maths, you should be aware that another way of writing “fourth root” of 1.20 is to write 1.20^(1/4) or 1.20^0.25

December 5, 2014 at 1:11 pm #217972sir , please help me wether what iam saying is correct or not ?

1+R = (1+r)^n

this is the formula . as here is r=20% = 0.20 in this i have no confusion . but n =4 or 0.25 sir here is only my confusion . it should be 4 ryt as it is for 4 yrs ?

please try to clear my confusion .

Thank you !!!December 5, 2014 at 1:30 pm #218379You are confusing big R and small r.

If r is the annual rate and R is the 4 year rate, then

(1+R) = (1+r) ^ 4

In this question we know the 4 year rate – 20%. So R = 0.20

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