Question

At what rate percent annum will rs 3000 amount to rs3993 in 3 years, the interest being compounded annualy.

Answer 1

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

$\green{\tt{\therefore{Rate\%=10\%}}}$

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

$\green{\underline \bold{Fiven :}} \\ \tt: \implies Principal(p) = 3000 \: rupees \\ \\ \tt: \implies Amount(A) =3993 \: rupees \\ \\ \tt: \implies Time(t) =3 \: years \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Rate\%(r) =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies A = p(1 + \frac{r}{100})^{t} \\ \\ \tt: \implies 3993 = 3000 \times (1 + \frac{r}{100} )^{3} \\ \\ \tt: \implies 3993 = 3000 \times ( \frac{100 + r}{100} )^{3} \\ \\ \tt: \implies \frac{3993}{3000} = (\frac{100 + r}{100}) ^{3} \\ \\ \tt: \implies 1.331 = ( \frac{100 + r}{100})^{3} \\ \\ \tt: \implies ( {1.1})^{3} = ( \frac{100 + r}{100} )^{3} \\ \\ \tt: \implies 1.1 = \frac{100 + r}{100} \\ \\ \tt: \implies 1.1 \times 100 = 100 + r \\ \\ \tt: \implies r = 110 - 100 \\ \\ \green{\tt: \implies r = 10\%}$

Answer 2

Given :-

At what rate percent annum will ₹ 3000 amount to ₹ 3993 in 3 years, the interest being compounded annually.

• Principal (P) = ₹ 3000

• Amount(A) = ₹ 3993

• Time(n) = 3 years

To find :-

The rate(r) %

Solution :-

We know,

$\tt{A=P(1+\frac{r}{100})^n }\\\\\tt{\implies 3993=3000(1+\frac{r}{100})^3 }\\\\\tt{\implies \frac{3993}{3000}=(1+\frac{r}{100})^3 }\\\\\tt{\implies \frac{1331}{1000}=(\frac{100+r}{100} )^3 }\\\\\tt{\implies (\frac{11}{10} )^3=(\frac{100+r}{100} )^3}\\\\\tt{\implies \frac{11}{10}=\frac{100+r}{100} }\\\\\tt{\implies 11=\frac{100+r}{10} }\\\\\\\sf{By\ cross\ multiplying:}\\\\\tt{\implies 110=100+r}\\\\\tt{\implies r=110-100}\\\\\tt{\boxed{r=10\%}}$

∴ So, the rate is 10 %.