# 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

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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**

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.