Question

find the difference between Simple interest and compound interest on Rs.12000 at 9%p.a. for 2 years coumponded annually?

Answer 1

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

$\green{\therefore{\text{Difference=97.2\:rupees}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Principle = 12000\:rupees} \\ \\ : \implies \text{Rate=9\%} \\\\ :\implies \text{Time=2\:years} \\ \\ \red{ \underline \bold{To \: Find : }} \\ \implies \text{Difference\:between\:simple\:and\:compond\:interest = ?}$

• According to given question :

$\bold{For \: Simple \: Interest} \\ : \implies S.I= \frac{p \times r \times t}{100} \\ \\ : \implies S.I = \frac{12000 \times 9 \times 2}{100} \\ \\ : \implies S.I = 120 \times 9 \times 2 \\ \\ \green{ : \implies \text{S.I= 2160 \: rupees}} \\ \\ \bold{For \: compound \: interest } \\ : \implies A = P(1 + \frac{r}{100} ) ^{t} \\ \\ : \implies A = 12000(1 + \frac{9}{100})^{2} \\ \\ : \implies A = 12000(1 + 0.09)^{2} \\ \\ : \implies A = 12000 \times (1.09)^{2} \\ \\ : \implies A = 12000 \times 1.1881 \\ \\ \green{: \implies \text{A = 14257.2 \: rupees}} \\ \\ : \implies C.I = a - p \\ \\ : \implies C.I= 14257.2 - 12000 \\ \\ \green{: \implies \text{C.I= 2257.2 \: rupees}} \\ \\ \bold{For \: difference} \\ : \implies Difference = C.I - S.I \\ \\ : \implies Difference = 2257.2 - 2160 \\ \\ \green{ : \implies \text{Difference = 97.2 \: rupees}}$

Answer 2

Question :--- find the difference between Simple interest and compound interest on Rs.12000 at 9%p.a. for 2 years coumponded annually ?

Solution (1) :---

Lets try it with Basic Method First ..

→ Principal = Rs.12000

→ Rate = 9% p.a.

→ Time = 2 years .

→ Simple interest = P*R*T/100

→ CI = A - P = [ P(1+r/100)^T ] - P

Putting values we get,

→ SI = 12000*9*2/100 = Rs.2160

→ CI = [12000*(1+9/100)² ] - 12000

= [ 12000*(109/100)*(109/100) ] - 12000

= 14257.2 - 12000

= Rs. 2257.2

Difference between CI and SI = 2257.2 - 2160 = Rs. 97.2 (Ans).

__________________________

✪✪ Shortcut Trick ✪✪

Difference b/w, CI and SI , when Time is 2 years is = (P * r²) / (100)²

Here ,

→ P given = Rs.12000

→ R given = 9%

So,

Required Difference = (12000*9*9)/(100*100) = Rs.97.2 (Ans).

Hence, Difference b/w CI and SI is Rs.97.2 .