At what rate percent compound interest per annum will Rs 640 amount to Rs 774.40 in 2 years?

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20 Questions 30 Marks 18 Mins

Given:

Principal = Rs 640

Amount = Rs 774.40

Time = 2 years

Concept:

A = P (1 + R/100)n

Calculation:

Let rate = R%

By using the formula,

⇒ A = P (1 + R/100)n

⇒ 774.40 = 640 (1 + R/100)2

⇒ (1 + R/100)2 = 774.40/640

⇒ (1 + R/100)2 = 484/400

⇒ (1 + R/100)2 = (22/20)2

⇒ By cancelling the powers on both sides, (1 + R/100) = (22/20)

⇒ R/100 = 22/20 – 1 = (22 - 20)/20 = 2/20

⇒ R = 100/10 = 10%

∴ Required Rate is 10% per annum.

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Given details are,

Principal = Rs 640

Amount = Rs 774.40

Time = 2 years

Let rate = R%

By using the formula,

A = P (1 + R/100)^n

774.40 = 640 (1 + R/100)^2

(1 + R/100)^2 = 774.40/640

(1 + R/100)^2 = 484/400

(1 + R/100)^2 = (22/20)^2

By cancelling the powers on both sides,

(1 + R/100) = (22/20)

R/100 = 22/20 – 1

= (22-20)/20

= 2/20

= 1/10

R = 100/10

= 10%

∴ Required Rate is 10% per annum

Given details are,

Principal = Rs 640

Amount = Rs 774.40

Time = 2 years

Let rate = R%

By using the formula,

A = P (1 + R/100)n

774.40 = 640 (1 + R/100)2

(1 + R/100)2 = 774.40/640

(1 + R/100)2 = 484/400

(1 + R/100)2 = (22/20)2

By cancelling the powers on both sides,

(1 + R/100) = (22/20)

R/100 = 22/20 – 1

= (22-20)/20

= 2/20

= 1/10

R = 100/10

= 10%

∴ Required Rate is 10% per annum.

At what rate percent compound interest per annum will Rs 640 amount to Rs 774.40 in 2 years?

Let the rate of interest be R % .
Then, 
\[A = P \left( 1 + \frac{R}{100} \right)^n \]
\[774 . 40 = 640 \left( 1 + \frac{R}{100} \right)^2 \]
\[ \left( 1 + \frac{R}{100} \right)^2 = \frac{774 . 40}{640}\]
\[ \left( 1 + \frac{R}{100} \right)^2 = 1 . 21\]
\[ \left( 1 + \frac{R}{100} \right)^2 = \left( 1 . 1 \right)^2 \]
\[\left( 1 + \frac{R}{100} \right) = 1 . 1\]
\[\frac{R}{100} = 0 . 1\]
R = 10
Thus, the required rate of interest is 10 % per annum.

Solution : Principal`(P)=Rs.640`<br>Amount`(A)=Rs.774.40`<br>Period`(n)=2` years<br>Let the rate of interest be `R` p.a.<br>`A/P=(1+R/100)^n`<br>`774.40/640=(1+R/100)^2`<br>`77440/(100times640)=(1+R/100)^2`<br>`121/100=(1+R/100)^2`<br>`1.21=(1+R/100)^2`<br>`(1.1)^2=(1+R/100)^2`<br>`(1+R/100)=(1.1)`<br>`R/100=0.1`<br>`R=10`<br>`therefore` The rate of interest be `10%` p.a.

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