# 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

aruv | Student

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

llltkl | Student

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.