Question

The difference between simple interest and
compound interest is Rs. 256 and the principal
amount has been invested for 2 years at the rate of
8%. What could be the principal amount?​

Answer 1

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

$\green{\tt{\therefore{Principal=40000\:rupees}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies C.I- S.I= 256 \: rupees \\ \\ \tt: \implies Rate\% (r)= 8\% \\ \\ \tt: \implies Time(t) = 2\: years \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Principal =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies S.I = \frac{p \times r \times t}{100} \\ \\ \tt: \implies S.I= \frac{p \times 8 \times 2}{100} \\ \\ \tt: \implies S.I=0.16p - - - - - (1) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies A= p(1 + \frac{r}{100} )^{t} \\ \\ \tt: \implies A= p \times (1 + \frac{8}{100} )^{2} \\ \\ \tt: \implies A =p \times (1 + 0.08)^{2} \\ \\ \tt: \implies A =p \times 1.1664p- - - - - (2) \\ \\ \bold{for \: compound \: interest} \\ \tt: \implies C.I=A - p \\ \\ \tt: \implies C.I= 1.1664p - p \\ \\ \tt: \implies C.I=0.1664p - - - - - (3) \\ \\ \bold{For \: Difference : } \\ \tt: \implies C.I- S.I = 256 \\ \\ \tt: \implies 0.1664p - 0.16p = 256 \\ \\ \tt: \implies 0.0064 p = 256 \\ \\ \tt: \implies p = \frac{256}{0.0064} \\ \\ \green{\tt: \implies p = 40000 \: rupees}$

Answer 2

The difference between simple interest and

compound interest is Rs. 256 and the principal

amount has been invested for 2 years at the rate of

8%. What could be the principal amount?

∆ Answer ∆

$\implies S.I.= \frac{P×P×T}{100}\\ \implies S.I= \frac{P×16}{100}\\ \implies S.I= 0.16p--eq(1)$

So,

$\rightarrow A=p 1+(\frac{r}{100})^n Amount = A=p×(1+0.08)^2 \\ \rightarrow A=p×1.664p---eq(2)$

★ Compound intrest (C.I)

$\rightarrow C.I=A-P\\ \rightarrow C.I= p-1.664p \\ \rightarrow C.I=0.0064p-------eq(3)$

→Difference

$\rightarrow C.I-S.I=256 \\ \rightarrow 0.1664p-0.16p=256\\\rightarrow p=\frac{256}{0.0064}\\\rightarrow p= 4000$

$\implies\red{\underline{\fbox{P= 4000}}}$