Question

By using the formula, find the amount and compound interest on:
1. 6000 for 2 years at 9% per annum compounded annually.​

Answer 1

Given :-

• 6000 for 2 years at 9% per annum compounded annually.

To find :-

• Amount and compound interest

Solution :-

As we know that

→ A = P(1 + R/100)ⁿ

Where " A " is amount, " P " is Principle, R is rate of interest and " n " is time.

• Principle (P) = Rs.6000

• Rate of interest (R) = 9%

• Time (T) = 2years

According to question

→ A = P(1 + R/100)ⁿ

Put the value of P, R, T and n

→ A = 6000(1 + 9/100)²

→ A = 6000(100 + 9/100)²

→ A = 6000(109/100)²

→ A = 6000 × 109/100 × 109/100

→ A = 60 × 109 × 109/100

→ A = 6 × 109 × 109/10

→ A = 6 × 109 × 10.9

→ A = Rs.7128.6

Hence,

• Amount is Rs.7128.6

Now,

→ Compound Interest = Amount - Principle

→ C.I = A - P

→ C.I = 7128.6 - 6000

→ C.I = Rs.1128.6

Therefore,

• Compound interest is Rs.1128.6

Answer 2

Given :

$\bullet\:\:\textsf{Principal = \textbf{Rs. 6000}}$

$\bullet\:\:\textsf{Time period = \textbf{2 years}}$

$\bullet\:\:\textsf{Rate of interest = \textbf{9 \%}}$

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Solution :

$:\implies\sf Amount = P \bigg\lgroup 1 + \dfrac{R}{100}\bigg\rgroup^{n}$

$:\implies\sf Amount = 6000 + \bigg\lgroup 1 + \dfrac{9}{100}\bigg\rgroup^2$

$:\implies\sf Amount = 6000 \big\lgroup 1 + 0.09\big\rgroup^2$

$:\implies\sf Amount = 6000 \big\lgroup 1.09\big\rgroup^2$

$:\implies\sf Amount = 6000 \big\lgroup 1.1881\big\rgroup$

$:\implies \underline{ \boxed{\sf Amount =Rs. \: 7128.60 }}$

$\therefore\:\underline{\textsf{The Amount is \textbf{Rs. 7128.60}}}.$

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⠀

$\dashrightarrow\:\:\sf Compound \: Interest = Amount - Principal$

$\dashrightarrow\:\:\sf Compound \: Interest = 71286.60 - 6000$

$\dashrightarrow\:\:\underline{\boxed{\sf Compound \: Interest = 1128.6}}$

$\therefore\:\underline{\textsf{The Compound Interest is \textbf{Rs. 112.86}}}.$

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$\boxed{\underline{\underline{\bigstar\:\bf\:Extra\:Shots\:\bigstar}}}$

$\tt 1) Profit = SP - CP$

$\tt 2) Loss = CP - SP$

$\tt 3) Profit\% = (Profit \:in \:Rs.)*100/CP$

$\tt 4) Loss\% = (Loss \:in \:Rs.)*100/CP$

$\tt 5) SP = CP*(100+P\%)/100$

$\tt 6) SP = CP*(100-L\%)/100$

$\tt 7) CP = SP*100/(100+P\%)$

$\tt 8) CP = SP*100/(100-L\%)$

$\tt 9) Discount =MP - SP$

$\tt 10) Discount\%=(Discount \:in \:Rs.)*100/MP$

$\tt 11) MP = SP*100/(100-D\%)$