Question

Find the difference between the simple interest and compound interest on Rs 16000 for

1 ½ years at 5% per annum, compound interest being reckoned half yearly?
​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{C.I-S.I=30.25\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Principal(p) = 16000 \: rupees \\ \\ \tt: \implies Time(t) =1\frac{1}{2} \: years \\ \\ \tt: \implies Rate\%(r) = 5\% \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies C.I - S.I= ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies S.I= \frac{p \times r \times t}{100} \\ \\ \tt: \implies S.I= \frac{16000 \times 5 \times \frac{3}{2} }{100} \\ \\ \tt: \implies S.I= \frac{16000 \times 5 \times 3}{100 \times 2} \\ \\ \green{\tt: \implies S.I =1200 \: rupees} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies A = p(1 + \frac{\frac{r}{2}}{100} )^{2t} \\ \\ \tt: \implies A =16000(1 + \frac{5}{2\times100} )^{2\times \frac{3}{2} } \\ \\ \tt: \implies A= 16000 \times (1 + 0.05)^{ {3} } \\ \\ \tt: \implies A=16000 \times 1.076890625 \\ \\ \green{\tt: \implies A =17230.25 \: rupees} \\ \\ \bold{For \: C.I : } \\ \tt: \implies ci = a - p \\ \\ \tt: \implies C.I = 17230.25- 16000 \\ \\ \green{\tt: \implies C.I =1230.25 \: rupees}\\ \\ \bold{For \: difference} \\ \tt: \implies Difference = C.I - S.I \\ \\ \tt: \implies Difference = 1230.25 - 1200 \\ \\ \green{\tt: \implies Difference =30.25 \: rupees}$

Answer 2

Given :-

Principal(p) =16000 rupees

Time (t) =3/2 years

Rate(r %) =5%

To FiND :-

Compound Interest(C. I) - Simple interest(S. I) =?

Solution :-

As we know,

$S. I \: = \frac{p \times r \times t}{100}$

$S. I \: = \frac{1600 0\times \frac{3}{2} \times 5 }{100}$

$S. I \: = 1200 \: rupees$

And the amount(A),

$A \: = p( { \frac{1 + \frac{r}{2} }{100}) }^{2 \times t}$

$A \: = 16000 {(1 + \frac{5}{2 \times 100} )}^{2}$

$A \: = 16000 \times 1.076890(approx) \\ A \: = 17230.25 \: rupees$

Now,

C. I = Amount (A) - principal (p)

C. I= 17230. 25 - 16000

C. I = 1230.25 rupees

Therefore according to the question, we have

C. I - S. I = 1230.25 - 1200

C. I - S. I = 30.25.

Hence the answer is 30.25.