Question

Find the compound interest on ₹10000 at 8% per annum for 6 months compounded quarterly.

Answer 1

Answer:

Step-by-step explanation:

Given,

Principal, P = 10,000

Rate of interest compounded quarterly, R = 8 % = 8/4 = 2 %

Time = 6 months = 6/12 × 4 = 2 quarters.

To Find,

Compound Interest

Formula to be used,

Amount, A = P × (1 + R/100)^n

Solution,

Putting all the values, we get

⇒ Amount, A = P × (1 + R/100)^n

⇒ Amount, A = 10,000 × (1 + 2/100)^2

⇒ Amount, A = 10,000 × (103/100)^2

⇒ Amount, A = 10,000 × 103/100 × 103/100

⇒ Amount, A = 10,000 × 1.03 × 1.03

⇒ Amount, A = Rs 10,609

Hence, the compound interest is 10,609.

Answer 2

$\sf Given \; that \begin{cases} & \sf{Rate \: of \: interest \: compounded \: quarterly. = \bf{8\% \: = \: 8/4 \: = \: 2\%}} \\ & \sf{Principal = \bf{10,000 \: Rupees}} \\ & \sf{Time = \bf{6 \: months \: = 6/12 \: \times 4 \: = \: 2}} \end{cases}$

$\sf To \; find \begin{cases} & \sf{Compound \: interest} \end{cases}$

$\sf Solution \begin{cases} & \sf{Compound \: interest = \bf{10,609 \: Rupees}} \end{cases}$

$\sf Using \; concept \begin{cases} & \sf{Compound \: Interest \: formula} \end{cases}$

$\sf Using \; formula \begin{cases} & \sf{Compound \: Interest = \bf{A \: = \: P \: \times \:(1+R/100)^{n}}} \end{cases}$

What does the question says ?

• This question says that the Principal is given as Rupees 10,000 and the rate of interest is given as 8% compounded quarterly means we have to divide 8 by 4 and we get 2. Afterwards the time is given as 6 months converted into quaters we get 6/12 × 4 = 2 quaters.

How to solve this question ?

• To solve this question we have to use the formula of compound interest that is A = P ×(1+R/100)ⁿ Now we have to put the values according to this formula. We get our final result easily and it's Rupees 10,609

Full solution :

Using formula of compound interest

↝ A = P ×(1+R/100)ⁿ

Where,

• A means amount
• P means Principal.
• R means Rate.
• ⁿ means time.

Putting the values,

↝ A = P ×(1+R/100)ⁿ

↝ A = 10,000 × (1+2/100)²

↝ A = 10,000 × (103/100)³

↝ A = 10,000 × 103 / 100 × 103 / 100

↝ A = 10,000 × 1.03 ×1.03

↝ A = 10,000 × 1.0609

↝ A = 10,609 Rs

Hence, Compounded interest is Rupees 10,609

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