Question

the compound interest on a certain sum of money at 5% ler annum for 2 years is 246.Calculate the sum and the aimple interest on the same sum for 3 years at 6% per annum​

Answer 1

Step-by-step explanation:

Given :-

The compound interest on a certain sum of money at 5% per annum for 2 years is 246.

To find:-

Calculate the sum and the simple interest on the same sum for 3 years at 6% per annum?

Solution :-

Given that :-

Rate of interest (R) = 5%

Time (T) = 2 years

Compound interest = Rs. 246

n = 2

Let the principle be Rs. P

We know that

Amount = P[1+(R/100)]^n

On Substituting these values in the above formula then

=>A = P[1+(5/100)]²

=> A = P[1+(1/20)]²

=> A = P[(20+1)/20]²

=> A = P(21/20)²

=> A = P(441/400)

=> A = 441P/400

The amount = Rs. 441P/400

We know that

Amount = Principle + Interest

=> 441P/400 = P+246

=> (441P/400)-P = 246

=> (441P-400P)/400 = 246

=> 41P/400 = 246

=> 41P = 246×400

=>P = 246×400/41

=> P = 6×400

=> P = 2400

Therefore, Principle = Rs. 2400

and

given that

Time = 3 years

Rate of interest = 6%

We know that

Simple Interest = PTR/100

On Substituting these values in the above formula then

=>SI = (2400×3×6)/100

=> SI = 24×3×6

=> SI = 432

Simple Interest = Rs. 432

Amount = P+I

=> Amount = 2400+432

=> Amount = 2832

Therefore, Amount = Rs. 2832

Answer:-

1) Principle for the given problem is

Rs. 2400

2) Simple Interest for the given problem is Rs. 432

3) mount for the given problem is

Rs. 2832

Used formulae:-

• A = P[1+(R/100)]^n

• A = Amount

• P = Principle

• R = Rate of Interest

• n = Number of times the compound interest is calculated

• SI = PTR/100

• T = Time

• A = P+I

• I = Interest

Answer 2

★ Appropriate Question ,

⠀⠀⠀The compound interest on a certain sum of money at 5% per annum for 2 years is 246.Calculate the sum and the simple interest on the same sum for 3 years at 6% per annum​

★ Given that ,

• The compound interest on a certain sum of money at 5% per annum for 2 years is 246

★ To be found ,

• Calculate the sum and the Simple interest on the same sum for 3 years at 6% per annum​

★ Formulas used ,

$\boxed{\begin{aligned}&\bullet\bf A = \rm{P \bigg( 1 +\dfrac{r}{100} \bigg) ^n }\\\\&\bullet \bf S.I = \rm{\dfrac{P \times R \times T}{100} }\\\end{aligned}}$

★ Where ,

• A stands for Amount
• P stands for Principal
• R stands for Rate
• T stands for Time
• N stands for No.of years

★ we know that ,

• Compound Interest = Amount - Principal
• 246 = Amount - Principal
• Amount = 246 + Principal

★ Here ,

• Amount = 246 + principal
• Time Period = 2 years
• Rate of Interest = 5%

★ According to the question ,

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

$:\implies \bf 246 + P = P\bigg ( 1 + \dfrac{5}{100} \bigg)^2$

$:\implies \bf 246 + P = P \bigg(1 +\dfrac{1}{20}\bigg) ^2$

$:\implies \bf 246 + P = P \bigg( \dfrac{21}{20} \bigg)^2$

$:\implies \bf 246 + P = P \bigg( \dfrac{441}{400} \bigg)$

$:\implies \bf 246 + P = P \times 1.1025$

$:\implies \bf 246 = 1.1025P - P$

$:\implies \bf 246 = 0.1025 P$

$:\implies \bf P =\cancel\dfrac{246}{0.1025}$

$:\implies \bf {\pink{\underline{\boxed{\pmb{\frak{ P = 2400}}}}\bigstar}}$

★ Henceforth ,

• The principal amount is Rs.2400

★ We need to find ,

$: \implies \bf S.I = \dfrac{P \times R \times T}{100}$

$: \implies \bf S.I = \dfrac{24\cancel{00}\times 3 \times 6}{1\cancel{00}}$

$: \implies \bf S.I = 24 \times 3 \times 6$

$:\implies \bf {\pink{\underline{\boxed{\pmb{\frak{S.I = 432}}}}\bigstar}}$

★ Now ,

${\bigstar{\underline{\boxed{\frak{ Amount = P + I }}}}}$

${\bigstar{\underline{\boxed{\frak{ Amount = 2832}}}}}$

${\red{\maltese}}\;{\underline{\underline{\textbf{\textsf{Therefore,}}}}}$

• The interest and the amount are Rs. 432 and 28342 respectively

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