You are provided with the following informationYou are provided an investment opportunity of investing $6000 for 3.5 years at an effective annual interest rate (EAR) of 13.36%. Interest is...

You are provided with the following information

You are provided an investment opportunity of investing $6000 for 3.5 years at an effective annual interest rate (EAR) of 13.36%. Interest is compounded semiannually. How much can you expect to receieve at the end of the 3.5 years?

A. 9305.55
B. 9305.95
c. 9466
D  10.037

I am quite confused here. Please solve this with financial calculator. I know the EAR is in annual, but do I need to convert it to APR with semmiannual compounding?

2 - P/YR
13.36% - Shift EFF
Shift Nom% = 12.47% (APR)

I would like to ask by doing so, is by 12.47% APR now a semmiannual rate or its still an annual rate? Do I need to divide it by 2 to get semiannual rate or this is in fact the semiannual rate now.

I tried 2 ways

3.5    13.36    6000
N    I/YR    PV        FV = 9305.95

But I realise I can get B answer as well.

7    6.47    6000    FV = 9305.55
N    I/YR    PV

Which is the correct input??


Asked on by natersuk

2 Answers | Add Yours

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

There is clearly some confusion in the wording of the question. Normally when we speak of effective annual interest rate, for a given period, it implies that it is the interest rate taking into consideration of the effect of compounding. For example,effective annual interest rate of 13.36 percent for a period of 3.5 years means that the the total interest after compounding for the 3.5 years period will be equal to:

(effective annual interest rate)x(period in years)

= 13.36x3.5 = 46.76

With this rate the total interest on $6000 will be

= 46.76 x (6000/100) = $2805.6

And the total amount of principal plus interest will be

= 6000 + 2805.6 = $8805.6

This answer does not tally with any of the options given.

As shown in answer posted above, the none of the options given in the problem tallies with right answer even if we assume that the given rate of interest (13.36) is to be compound.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

 

The principal =$6000.

The annual rate of interest =13.36%

Therefore the  rate of semi annual interest = 13.36/2=6.68% or 0.0668 per dollar.

The principal P  for n compounding periods with  rate of interest x for the compounding period will grow to an amount A given by: A = P(1+x)^n

Here x= 13.36%/2=6.68% 0r 0.668 per dollar. and n=3.5*2=7

The compound interest with principal for 3.5 yrs or seven semi annuals is 6000(1.0668)^(3.5*2)= 6000(1.0668^7)=$9434.79. None of the choices given are correct.The choice at c is only nearest. That is the solution.The problem for you is that correct answer has to be chosen from all the wrong answers given. To add to the confusion, there are nearly equal choices at A and B which appears correct for you, but both are not correct.There is nothing said  about interest other than EAR. So why introduce  different APR . So work it on EAR/2 for semiannual compounding.

 

To get the amount at A. 9305.55 the amount you should have an effective annual interest rate {[(9305.55/6000)^1/7]-1}*2*100%=12.94%

To get the amount at B. 9305.95 you should have the effective annual interest rate {[(9305.55/6000)^(1/7)]-1}*2*100%=12.94%.

To get the amount at  c. 9466, you should have the effective annual interest rate 13.46% nearly.

You get the amount at D  10,037 ( revised by me instead of 10.037 to be realistic) , if the effective annual interest rate is 15.2543% approximately.

You  worked out in two methods . (1) Taking 3.5 years and compounding period as one year , principle $6000 and EAR =13.36% and obtained a value of 9305.95. but it is not the solution of the original problem, though it tallies with the choice C.  (2) Again there is a calculation  of compounding semi annually with a semiannual interest 6.47 and getting an amount $9305.55. Both methods are different and not the solution for the original problem.

The solution of the original problem is as given in bold type.

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