Question

Q) What is the compound interest on $ 64,000 for $1 \frac{1}{2}$ years at 5% p.a. compounded half yearly?
Please answer with steps...

Answer 1

Given:

$64000 is compounded half-yearly for $1\frac{1}{2}$ years at 5%p.a

To Find:

The compound interest

Solution:

To find the compound interest which is being compounded half-yearly we will use a formula i.e.

                                          $A=P(1+\frac{r}{n})^{nt}$

                                where,

                                           $A$=Final amount

                                           $r$=rate of interest

                                           $t$=time period

                                           $n$=total number of times compounded

Now putting all the values in the formula

$P$=64000

$r$=5%

$t$=1.5 years

$n$=2

Therefore

                                  $A=64000(1+\frac{0.05}{2})^{2*1.5} \\=64000(1.025)^{3} \\=64000*1.07689\\=68921$

So the final is $68921

therefore

CI=Final amount-initial amount

CI=68921-64000

CI=4921$

Hence, the compound interest is $4921.