Question

calculate the amount and compound interest on ₹90, 000 at the rate of 4% p. a. compound annually for 2 years
​

Answer 1

Given :

• Principal = ₹90000
• Rate = 4% p.a.
• Time = 2 years
• Compound interest is applied annually

To find :

• Amount
• Compound interest

At end of two years

Forumula used :

$\sf \bullet\: A = P\bigg( 1 + \dfrac{R}{100} \bigg)^{T}$

$\sf \bullet\: A = P + C.I.$

Here,

• T = time
• A = amount after time T
• P = principal
• R = Rate%
• C.I. = Compound interest after time t

Solution :

First of all we will calculate Amount after two years by using above formula

$\sf \bullet\: A = 90000\bigg( 1 + \dfrac{4}{100} \bigg)^{2} \\ \\ \sf \implies\: A = 90000\bigg( \dfrac{(1 \times 100) + (4 \times 1)}{100} \bigg)^{2} \\ \\ \sf \implies\: A = 90000\bigg( \dfrac{100 + 4}{100} \bigg)^{2} \\ \\ \sf \implies\: A = 90000 \times \bigg( \dfrac{104}{100} \bigg)^{2} \\ \\ \sf \implies\: A = 90000 \times \bigg( \dfrac{ {104}^{2} }{100 ^{2} } \bigg) \\ \\ \sf \implies\: A = 90000 \times \: \dfrac{ 10816}{10000 } \\ \\ \sf \implies\: A =10816 \times \: \dfrac{ 90000}{10000 } \\ \\ \sf \implies\: A =10816 \times \: 9 \\ \\ \sf \implies\: A \: = \: 97344$

Amount = ₹97344

_______________________________________________

Amount = Principal + C.I.

➝ C.I. = Amount - principal

➝ C.I. = ₹97344 - ₹90000

➝ C.I. = ₹7344

_______________________________________________

ANSWER :

• Amount = ₹97,344
• Compound interest = ₹7,344

Answer 2

Given:

• P (Principle) = ₹90000

• R (rate) = 4%

• T = 2years

To find:

• Amount

• Compound interest

Solution:

For first year

here:

• P = ₹90000

• R = 4%

• T = 1 year

We know:

$\bigstar \boxed{ \rm{}Simple \: Interest = \frac{P \times R \times T}{100} }$

By using this formula we can find value of Simple interest

$\dashrightarrow\sf{}Simple \: Interest = \dfrac{P \times R \times T}{100}$

$\dashrightarrow\sf{}Simple \: Interest = \dfrac{90000 \times 4 \times 1}{100}$

$\dashrightarrow\sf{}Simple \: Interest = \dfrac{900 \cancel{00 }\times 4 \times 1}{1 \cancel{00} }$

$\dashrightarrow\sf{}Simple \: Interest = \dfrac{900\times 4 \times 1}{1}$

$\dashrightarrow\sf{}Simple \: Interest = 900\times 4 \times 1$

$\dashrightarrow\sf{}Simple \: Interest = 900\times 4$

$\dashrightarrow\sf{}Simple \: Interest =Rs \: 3600$

To find Amount:

We know:

$\bigstar \boxed{ \rm{}Amount = Simple \: Interest + Principle}$

By using this formula we can find value of Amount

$\dashrightarrow \sf{}Amount = Simple \: Interest + Principle$

$\dashrightarrow \sf{}Amount = 3600 + 90000$

$\dashrightarrow \sf{}Amount = Rs93600$

For 2 year:

here:

• P = ₹93,600

• R = 4%

• T = 1 year

we know:

$\bigstar \boxed{ \rm{}Simple \: Interest = \frac{P \times R \times T}{100} }$

$\dashrightarrow\sf{}Simple \: Interest = \dfrac{P \times R \times T}{100}$

$\dashrightarrow\sf{}Simple \: Interest = \dfrac{93600 \times 4 \times 1}{100}$

$\dashrightarrow\sf{}Simple \: Interest = \dfrac{936\cancel{00} \times 4 \times 1}{1\cancel{00}}$

$\dashrightarrow\sf{}Simple \: Interest = \dfrac{936\times 4 \times 1}{1}$

$\dashrightarrow\sf{}Simple \: Interest = 936\times 4 \times 1$

$\dashrightarrow\sf{}Simple \: Interest = 936\times 4$

$\dashrightarrow\sf{}Simple \: Interest = Rs3744$

To find Amount:

We know:

$\bigstar \boxed{ \rm{}Amount = Simple \: Interest + Principle}$

$\dashrightarrow \sf{}Amount = Simple \: Interest + Principle$

$\dashrightarrow \sf{}Amount = 3744+93600$

$\dashrightarrow\underline {\boxed {\sf{}Amount =Rs~ 97344}}$

To find Compound interest:

$\dashrightarrow \sf{}Compound \: interest = Amount - Principle$

$\dashrightarrow \sf{}Compound \: interest = 97344 - 90000$

$\dashrightarrow \underline {\boxed {\sf{}Compound \: interest = Rs~7344 }}$