Question

find the principal which amounts to rupees 17640 at the rate of 5p.c.p.a compound annually for two years?​

Answer 1

Answer:

• The Principal is Rs 16000.

Step-by-step explanation:

Given that:

1. Amount = Rs 17640
2. Rate of interest = 5% p.a.
3. Time = 2 years

To Find:

• Principal

Formula used:

In compound interest.

• A = P(1 + R/100)ᵀ

Where,

• A = Amount
• P = Principal
• R = Rate of interest
• T = Time

Finding the principal:

Substituting the given values in formula.

⟶ 17640 = P(1 + 5/100)²

⟶ 17640 = P(1 + 0.05)²

⟶ 17640 = P(1.05)²

⟶ 17640 = P × 1.05 × 1.05

⟶ 17640 = 1.1025P

⟶ P = 17640/1.1025

⟶ P = 16000

∴ Principal = Rs 16000

Answer 2

Given :-

Amount = 17640

Rate = 5%

Time = 2 years

To Find :-

Principal

Solution :-

We know that

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

$\sf 17640 = p{\bigg(1 + \dfrac{5}{100} \bigg)}^{2}$

$\sf 17640 = p{\bigg(\dfrac{100+5}{100}\bigg)^{2}}$

$\sf 17640 = p{\bigg(\dfrac{105}{100}\bigg)}^{2}$

$\sf 17640 = p{\bigg(\dfrac{21}{20}\bigg)^{2}}$

$\sf 17640 = p + \dfrac{20}{21} \times \dfrac{20}{21}$

$\sf 17640 = p \times\dfrac{441}{400}$

$\sf p = \dfrac{17640\times 400}{441}$

$\sf p = 40 \times 400$

$\sf Principal = 16000\star$