Find the interest on $10 000 at 16% per annum for 2 years, compounded half-yearly. Give the answer correct to the nearest dollar.  A.    $1 664          B.    $3...

Find the interest on $10 000 at 16% per annum for 2 years, compounded half-yearly. Give the answer correct to the nearest dollar.
 A.    $1 664         

B.    $3 456         

C.    $3 605         

D.    $7 424   

E.    $8 106

2 Answers | Add Yours

aruv's profile pic

aruv | High School Teacher | (Level 2) Valedictorian

Posted on

Find the interest on $10 000 at 16% per annum for 2 years, compounded half-yearly. Give the answer correct to the nearest dollar.

P=10000

time T=2 years

conversion period =1/2 years

no. of conversion = 2/(1/2)=4

rate of interest =16 % perannum

=8% half yearly

`CI=A-P`

`=P(1+8/100)^4-P`

`=10000(1+.08)^4-10000`

`=10000((1.08)^4-1)`

`=10000(1.36048896-1)`

`=10000(.3605)`

`=3605`

Thus compound interest is $3605

Correct answer is C

llltkl's profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

The compounding amount of a savings scheme (principal+interest) is given by:

` A=P(1+r)^n`

(where P is the principal amount, r the rate of interest and n, the number of completed terms).

Plugging in the values here,

`A=$10000(1+0.16)^2=$13456`

Therefore, interest accrued=A-P=13456-10000=$3456

Option B has the correct answer.

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llltkl's profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

I am sorry for overlooking the half-yearly compounding portion of the question!

The rate of interest should be 0.16/2=0.08 per term.

And the number of terms: 2*2=4

So, the amount `A= $10000*(1+0.08)^4=$13604.89~~$13605`

Interest accrued=$13605-$10000=$3605

Correct answer is at option C.

mathewww's profile pic

mathewww | High School Teacher | (Level 1) Honors

Posted on

Sorry! I overlooked the half-yearly compounding portion.

The rate of interest would be 0.16/2=0.08, and the number of terms =2*2=4.

So the amount should be `A=$10000(1+0.08)^4=$13604.89~~$13605`

So, Interest accrued=A-P=$(13605-10000)=$3605

The correct answer is therefore, at Option C.

Please ignore my earlier choice.

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