Question

if compound interest is 1449 rupees for 2year at a rate of 7percent per annum find the value of simple interest?​

Answer 1

Answer:

• The value of simple interest is Rs 1400.

Step-by-step explanation:

Given that:

• Compound interest = Rs 1449
• Time = 2 years
• Rate of interest = 7% per annum

To Find:

• The value of simple interest.

Let us assume:

• The principal be x.

Formula used:

1. SI = (P × R × T)/100
2. CI = P(1 + R/100)ᵀ - P

Where,

• SI = Simple interest
• CI = Compound interest
• P = Principal
• R = Rate of interest
• T = Time

Finding the principal:

⟶ CI = P(1 + R/100)ᵀ - P

Substituting the values.

⟶ 1449 = x(1 + 7/100)² - x

⟶ 1449 + x = x(1 + 0.07)²

⟶ 1449 + x = x(1.07)²

⟶ 1449 + x = x × 1.07 × 1.07

⟶ 1449 + x = 1.1449x

⟶ 1.1449x - x = 1449

⟶ 0.1449x = 1449

⟶ x = 1449/0.1449

⟶ x = 10000

∴ Principal = Rs 10000

Finding the simple interest:

⟶ SI = (P × R × T)/100

Substituting the values.

⟶ SI = (10000 × 7 × 2)/100

⟶ SI = 140000/100

⟶ SI = 1400

∴ Simple interest = Rs 1400

Answer 2

Given : The compound interest is Rs. 1449 for 2 years at a rate of 7 % p.a.

Exigency To Find : The Value of Simple Interest.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❒ Let's consider the Principal be P .

⠀⠀⠀⠀⠀Finding Principal for Simple interest :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Compound \:Interest \:\::P\bigg( 1 + \dfrac{R}{100}\bigg) ^T - P }\bigg\rgroup$

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀Here P is the Principal, R is the Rate of Interest , T is the Time & we have given with the Compound Interest is Rs.1449 .

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

⠀⠀⠀⠀⠀

$\qquad \longmapsto \sf{ 1449 = P \bigg( 1 + \dfrac{7}{100} \bigg)^2 - P }$

$\qquad \longmapsto \sf{ 1449 = P \bigg( 1 + 0.07 \bigg)^2 - P }$

$\qquad \longmapsto \sf{ 1449 = P \bigg( 1.07 \bigg)^2 - P }$

$\qquad \longmapsto \sf{ 1449 + P = P \bigg( 1.07 \bigg)^2 }$

$\qquad \longmapsto \sf{ 1449 + P = P \times 1.1449 }$

$\qquad \longmapsto \sf{ 1449 + P = 1.1449P }$

$\qquad \longmapsto \sf{ 1449 = 1.1449P - P}$

$\qquad \longmapsto \sf{ 1449 = 0.1449P }$

$\qquad \longmapsto \sf{ \dfrac{1449}{0.1449} = P }$

$\qquad \longmapsto \frak{\underline{\purple{ P =Rs. 10,000 }} }\bigstar$

⠀⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀⠀$\therefore{\underline{\mathrm {\:Principal \: \:is\:\bf{Rs.\: 10,000}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Finding Simple- Interest :

$\qquad \dag\:\:\bigg\lgroup \sf{ Simple \:Interest \:\:: \dfrac{P \times R\times T }{100} }\bigg\rgroup$

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀Here P is the Principal, R is the Rate of Interest & T is the Time

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

⠀⠀⠀⠀⠀

$\qquad \longmapsto \sf S.I = \dfrac{10000 \times 7 \times 2 }{100}$

$\qquad \longmapsto \sf S.I = \dfrac{100\cancel {00} \times 7 \times 2 }{\cancel{100}}$

$\qquad \longmapsto \sf S.I = 100 \times 7 \times 2$

$\qquad \longmapsto \sf S.I = 700 \times 2$

$\qquad \longmapsto \frak{\underline{\purple{ S.I =Rs. 1400 }} }\bigstar$

⠀⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Simple \:Interest \: \:is\:\bf{Rs.\: 1400}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀