Question

find the amount and the compound interest for rupees 10,000 for 1 year at the rate of 8% per annum compounded quarterly​

Answer 1

Answer:

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Answer 2

$\bf \small \underline {\underline{Question : }}$

Find the amount and the compound interest for ₹10,000 for 1 year at the rate of 8% per annum compounded quarterly.

❒ Given :

• Principal (P) = ₹10,000
• Time (T) = 1 year = 4 quarters
• Rate (R) = 8% per annum = 2% per quarter.

❒ To Do :

• Find the amount for the given question.
• Find the compound interest for the given question.

❒ Step by step Solution :

Taking note of the given parameters,

$\sf{{ The \: interest \: for \: the \: first \: quarter \: is \: \: \frac{₹10000 \times 2 \times 1}{100} \: = }{ \:₹200 }}$

➻ The amount at the end of the first quarter is ₹10,000 + ₹200 = ₹10,200.

➯ The principal for the second quarter is ₹10,200.

$\sf{{ So, \: the \: interest \: for \: the \: second \: quarter \: is \: \: \frac{₹10200 \times 2 \times 1}{100} = }{ \:₹204 }}$

➻ The amount at the end of the second quarter is ₹10,200 + ₹204 = ₹10,404

➯ The principal for the third quarter is ₹10,404.

$\sf{{So, \: the \: interest \: for \: the \: third \: quarter \: is \: \: \frac{₹10404 \times 2 \times 1}{100} \: = \: ₹208.08}{ \: }}$

➻ The amount at the end of the third quarter is ₹10,404 + ₹208.08 = ₹10,612.08

➯ The principal for the fourth quarter is ₹10,612.08

$\sf{{ So, \:the \: interest \: for \: }{ the\: fourth \: quarter \: is \: \: \frac{₹10612.08 \times 2 \times 1}{100} = ₹212.2416 \: ≈ \: ₹212.24 }}$

Hence,

∴ Final amount = ₹10,612.08 + ₹212.24 = ₹10,824.32

We know that,

Compund interest = (final amount) - (original principal)

Therefore,

∴ ₹10,824.32 - ₹10,000 = ₹824.32

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Remember these :

• To calculate the compund interest, first calculate the interest for the period of time it is compounded . Add this to the original principal to get the principal for the next period of time, and calculate the interest on this principle for the next period of time. Then, add this interest to the principal for the second period of time . Repeat the process for the required period.
• Compund interest = (final amount) - (original principal)

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