Question

Surabhi borrowed a sum of Rs 12000 from a finance company to purchase a
refrigerator. If the rate of interest is 5% per annum compounded annually, calculate
the compound interest that Surabhi has to pay to the company after 3 years​

Answer 1

$\sf\large\underline\blue{Given:-}$

$\tt{\implies Principal=Rs.12000}$

$\tt{\implies Rate\:of\: interest=5\%}$

$\tt{\implies Time=3\: years}$

$\sf\large\underline\blue{To\: Find:-}$

$\tt{\implies Interest\:paid\:_{(by\:Surabhi)}=?}$

$\sf\large\underline\blue{Solution:-}$

To calculate Interest paid by Surabhi to the company after 3 years at the rate of 5% compounded annually. At first we have to find amount by applying formula then calculate Interest.

$\sf\large\underline\blue{Formula\:Used:-}$

$\tt\red{\implies A=P\bigg(1+\dfrac{r}{100}\bigg)^n}$

$\tt{\implies A=12000\bigg(1+\dfrac{5}{100}\bigg)^3}$

$\tt{\implies A=12000\bigg(\dfrac{100+5}{100}\bigg)^3}$

$\tt{\implies A=12000\bigg(\dfrac{105}{100}\bigg)^3}$

$\tt{\implies A=12000*(1.05)^3}$

$\tt{\implies A=12000*1.157625}$

$\tt{\implies A=13891.5}$

• Now calculate Interest, here:-]

$\tt\purple{\implies I=A-P}$

$\tt{\implies I=13891.5-12000}$

$\tt{\implies I=1891.5}$

$\sf\large{Hence,}$

$\tt\green{\implies Interest\:paid\:_{(by\:Surabhi)}=1891.5}$

$\tt\green{\implies Amount\:paid\:_{(by\:Surabhi)}=13891.5}$

$\sf\large\underline\blue{Some\: Important\: Formula:-}$

$\sf{\implies CI=P\bigg(1+\dfrac{r}{100}\bigg)^{n}-P}$

$\tt{\implies SI=\dfrac{P\times\:T\times\:R}{100}}$

$\tt{\implies A=P\bigg(1+\dfrac{RT}{100}\bigg)}$

$\tt{\implies R=\dfrac{SI*100}{P*T}}$

$\tt{\implies T=\dfrac{SI*100}{P*R}}$

$\tt{\implies Amount=Principal+Interest}$

Answer 2

Answer:

Given :-

• Surabhi borrowed a sum of Rs 12000 from a finance company to purchase a refrigerator and the rate of Interest is 5% per annum compound annually.

To Find :-

• What is the compound interest that Surabhi to pay to the company after 3 years.

Formula Used :-

❶ To find amount we know that,

${\red{\boxed{\large{\bold{A =\: P\bigg(1 + \dfrac{r}{100}\bigg)^{n}}}}}}$

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• n = Time

❷ To find compound interest we know that,

${\red{\boxed{\large{\bold{C.I =\: A -\: P}}}}}$

where,

• C.I = Compound Interest
• A = Amount
• P = Principal

Solution :-

❶ First we have to find the amount,

Given :

• Principal (P) = Rs 12000
• Rate of Interest (r%) = 5%
• Time (n) = 3 years

According to the question by using the formula we get,

⇒ $\sf A =\: 12000\bigg(1 + \dfrac{5}{100}\bigg)^{3}$

⇒ $\sf A =\: 12000\bigg(\dfrac{100 + 5}{100}\bigg)^{3}$

⇒ $\sf A =\: 12000\bigg(\dfrac{105}{100}\bigg)^{3}$

⇒ $\sf A =\: 12{\cancel{00}}{\cancel{0}} \times \dfrac{105}{\cancel{100}} \times \dfrac{105}{10\cancel{0}} \times \dfrac{105}{100}$

⇒ $\sf A =\: \dfrac{12 \times 105 \times 105 \times 105}{10 \times 100}$

⇒ $\sf A =\: \dfrac{138915\cancel{00}}{10\cancel{00}}$

⇒ $\sf A =\: \dfrac{138915}{10}$

➠ $\sf\bold{\green{A =\: Rs\: 13891.5}}$

Hence, the amount is Rs 13891.5 .

❷ Now we have to find the compound interest that Surabhi has to pay to the company,

Given :

• Amount (A) = Rs 13891.5
• Principal (P) = Rs 12000

According to the question by using the formula we get,

↦ $\sf C.I =\: Rs\: 13891.5 -\: Rs\: 12000$

➦ $\sf\bold{\purple{C.I =\: Rs\: 1891.5}}$

$\therefore$ The compound interest that Surabhi has to pay to the company after 3 years is Rs 1891.5 .