Question

find the compound interest and amount of principle of rs 6000 for 5 years compounded anually at 6%​

Answer 1

Solution!!

The concept of compound interest has to be used here. The principal, rate of interest and time is given. We have to find the compound interest and the amount.

We can find it with formula and without formula too. In this case, the process will be lengthy and their will be high chances of making mistakes and it will consume too much time. So, it's better to find it out with the formula.

Principal (P) = Rs 6000

Time (n) = 5 years

Rate of interest (R) = 6%

Amount = P(1 + (R/100))⁵

Here 5 is the time (n).

Amount = 6000(1 + (6/100))⁵

Amount = 6000(106/100)⁵

Amount = 6000(53/50)⁵

Amount = 6000 × (53/50) × (53/50) × (53/50) × (53/50) × (53/50)

Amount = 6 × (53/5) × (53/5) × (53/5) × (53/50) × (53/50)

Amount = Rs 8029.35

Compound interest (CI) = Amount - Principal

CI = Rs 8029.35 - Rs 6000

CI = Rs 2029.35

Answer 2

Answer:

${ \large\underline\red{\sf{\pmb{Given}}}}$

• ➛ Principal = 6000
• ➛ Time = 5 years
• ➛ Rate = 6%

$\large \underline\red{\sf \pmb{To \: Find }}$

• ➛ Amount of principle
• ➛ Compound interest

$\large \underline\red{ \sf \pmb{Using \: Formulas }}$

$\bigcirc\underline {\boxed{ \sf{Amount = P\bigg(1 + { \dfrac{ R}{100} \bigg) }^{T} }}}$

$\: \: \: \large\circ\underline{ \boxed {\sf{C.I =A - P}}}$

Where

• ➟ R = Rate
• ➟ T = Time
• ➟ C.I = Compound Interest
• ➟ A = Amount
• ➟ P = Principle

$\large \underline\red{ \sf \pmb{Solution}}$

$\bigstar \: \underline\frak \pink{Firstly,finding \: the \: amount}$

${ \implies\sf{Amount = P\bigg(1 + { \dfrac{ R}{100} \bigg) }^{T} }}$

• Substituting the values

${ \implies\sf{Amount = 6000 \bigg(1 + { \dfrac{ 6}{100} \bigg) }^{5} }}$

${ \implies\sf{Amount = 6000 \bigg({ \dfrac{100 + 6}{100} \bigg) }^{5} }}$

${ \implies\sf{Amount = 6000 \times \bigg( {\cancel{ \dfrac{106}{100}}\bigg)}^{5}}}$

${ \implies\sf{Amount = 6000 \times { \big(1.06 \big)}^{5} }}$

${ \implies\sf{Amount = 6000 \times 1.06 \times 106 \times 1.06 \times 1.06 \times 1.06}}$

$\implies\sf{Amount = 8029.35 \: \big(Approx \big)}$

$\large \star\underline{ \boxed{\sf \purple{Amount = Rs.8029.35}}}$

$\bigstar \: \underline \frak \pink{Now, finding \: the \: Compound \: Interest }$

$\implies {\sf{C.I =A - P}}$

• Substituting the values

$\implies {\sf{C.I =8029.35 -6000}}$

$\implies {\sf{C.I =Rs.2029.35}}$

$\large\star \underline {\boxed{ \sf \purple{Compound \: Interest = Rs.2029.35}}}$

• ➛ Henceforth,The amount is Rs.8029.35 and the Compound Interest is Rs.2029.35

$\large \underline\red{\sf \pmb{More \: Useful \: Formulae}}$

★ Formula of Simple Interest (S.I)

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

★ Formula of Principle(P) if Amount and Interest given

• $: \implies\sf \purple{P=Amount - Interest}$

★ Formula of Principle (P) if Interest,time and rate given

• $: \implies\sf \purple{P = \dfrac{Interest \times 100 }{Time \times Rate} }$

★ Formula of Principle (P) if amount,time and rate given

• $: \implies\sf \purple{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)} }$

★ Formula of Amount if Principle (P) and Interest (I) given

• ${: \implies \sf \purple{Amount = Principle + Interest }}$