Question

Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest. At the end of 2 years, the amount in the bank account is £1379.02. Calculate r .

Answer 1

Answer:

$\large{\underline{\boxed{\mathfrak\blue{Rate \: of \: interest = 7.2\%}}}}$

Step-by-step explanation:

Given:-

• Principal (p) = £1200
• Time(n) = 2 years.
• Compounded amount (CA) = £1379.02

To find:-

• Rate of interest (r) = ?

We know,

$\star\:{\boxed{\mathfrak\green{Compound \: interest = Amount - Principal}}}$

⇒ Compound interest = £(1379.02 - 1200)

⇒ Compound interest = £179.02

$\rule{100}1$

Now,we know,

$\star\:{\boxed{\mathfrak\purple{CI = P(1 + r)^n - P}}}$

• Putting values:-

$\twoheadrightarrow\sf 179.02 = 1200(1 + r)^2 - 1200 \\\\\twoheadrightarrow\sf 179.02 + 1200 = 1200(1 + r)^2 \\\\\twoheadrightarrow\sf 1379.02 = 1200(1 + r)^2 \\\\\twoheadrightarrow\sf (1 + r)^2 =\dfrac{1379.02}{1200}\\\\\twoheadrightarrow\sf 1 + r = \sqrt{1.14918}\\\\\twoheadrightarrow\sf 1 + r = 1.072 \\\\\twoheadrightarrow\sf r = 1.072 - 1 \\\\\twoheadrightarrow\sf r = 0.072 \\\\\twoheadrightarrow\sf r = \dfrac{7.2}{100}\\\\\twoheadrightarrow\large{\underline{\boxed{\sf\blue{r = 7.2\%}}}}$

$\therefore{\boxed{\rm{Rate \: of \: interest (r) = 7.2\%}}}$

Answer 2

let's do it with second method...... without using the formula

amount with interest on first year =1200+1200×r/100=1200+12r

now, another , interest of r percent will be on 1200+12r

so,total amount at the end of 2 years=(1200+12r)+(1200+12r)×r/100

so,

(1200+12r)+(1200+12r)×r/100=1379.02

(1200+12r)(1+r/100)=1379.02

(1200+12r)(100+r)×1/100=1379.02

(1200+12r)(100+r)=137902

120000+1200r+1200r+12r^2=137902

12r^2+2400r=17902

6r^2+1200r=8951

6r^2+1200r-8951=0

using quadratic formula,,we will get

r={-1200+-(1440000-24×8951)^1/2}/1/12

r={-1200+-(1225176)^1/2}1/12

solving this equation,u will get

r=7.267

=7.26(approx..)