Question

Find the difference between the compound interest and simple interest on RS 15000 for 2 years at the rate of 5 percent p.a. compounded annually.​

Answer 1

S O L U T I O N :

Given :

• Principal, (P) = Rs.15000
• Time, (n) = 2 years
• Rate, (R) = 5% p.a

Explanation :

As we know that formula of the compound annually & simple interest :

• A = P(1 + R/100)^n
• S.I. = PRT/100

A/q

➲ A = P(1 + R/100)^n

➲ A = 15000(1 + 5/100)²

➲ A = 15000(1 + 1/20)²

➲ A = 15000(20 + 1/20)²

➲ A = 15000(21/20)²

➲ A = 15000 × 21/20 × 21/20

➲ A = 15000 × 441/400

➲ A = 37.5 × 441

➲ A = Rs.16537.5

Now, as we know that compound Interest;

➲ C.I. = Amount - Principal

➲ C.I. = Rs.16537.5 - Rs.15000

➲ C.I. = Rs.1537.5

___________________________

➲ Simple Interest = PRT/100

➲ Simple Interest = 15000 × 5 × 2/100

➲ Simple Interest = Rs.(150 × 10)

➲ Simple Interest = Rs.1500

Now,

Difference, (D) = C.I. - S.I

Difference, (D) = Rs.1537.5 - Rs.1500

Difference, (D) = Rs.37.5 .

Answer 2

Answer:

Given :-

❶ For compound interest :-

• Principal (P) = Rs 15000
• Rate of Interest (r%) = 5 %
• Time (n) = 2 years

❷ For simple interest :-

• Principal (P) = Rs 15000
• Rate of Interest (r%) = 5 %
• Time (t) = 2 years

To Find :-

• What is the difference between the compound .

Formula Used :-

❶ Compound Interest :-

$\boxed{\bold{\large{\mathtt{Amount\: =\: P(1 + \dfrac{r}{100})^{n}}}}}$

❷ Simple Interest :-

$\boxed{\bold{\large{\mathtt{S.I = \dfrac{Prt}{100}}}}}$

❸ Different between compound interest and simple interest :-

$\boxed{\bold{\large{\mathtt{Compound\: interest - Simple\: Interest}}}}$

Solution :-

❶ Compound Interest

Given :-

• P = Rs 15000
• r% = 5 %
• n = 2 years

According to the question by using the formula we get,

⇒ Amount = 15000 (1 + $\dfrac{5}{100}$ )²

⇒ Amount = 15000 (1+ $\sf\dfrac{\cancel{5}}{\cancel{100}}$ )²

⇒ Amount = 15000 (1 + $\dfrac{1}{20}$ )²

⇒ Amount = 15000 ( $\dfrac{21}{20}$ )²

⇒ Amount = 15000 × $\dfrac{21}{20}$ × $\dfrac{21}{20}$

⇒ Amount = $\dfrac{66150}{4}$

➠ Amount = 16537.5

Now, we have to find the compound interest,

✦ Compound Interest = Amount - Principal ✦

↦ Compound Interest = 16537.5 - 15000

➟ Compound Interest = Rs 1537.5

❷ Simply Interest

Given :

• P = Rs 15000
• r% = 5 %
• t =. 2 years

According to the question by using the formula we get,

⇒ S.I = $\dfrac{15000 \times 5 \times 2}{100}$

⇒ S.I = $\dfrac{150000}{100}$

⇒ S.I = $\sf\dfrac{\cancel{150000}}{\cancel{100}}$

➠ S.I = Rs 1500

❸ Now, we have to find the difference between C.I and S.I we get,

⇒ Difference = 1537.5 - 1500

➥ Difference = Rs 37.5

$\therefore$ The difference between Compound Interest and Simple Interest is Rs 37.5 .