Question

find the compound interest on rupees 8000 to for one year at 12% per annum if the interest is compounded quarterly. ​

Answer 1

Given

• Principal = Rs. 8000.
• Rate of Interest = 12% p.a.
• Time = 1 year.
• Compounded = Quarterly

To Find

• Compound Interest.

Formula To Be Used

• I = P × R × T/100.
• A = P + I.
• C.I. = Final Amount - Original Principal.

Solution

In this question we can see that we are given principal, rate and time and with this information we have to calculate compound interest. We can also see that the interest is compounded quarterly.

Since interest is compounded quarterly, so we have to divide the rate by 4 and multiply the time by 4.

Therefore,

• Principal = Rs. 8000.
• Rate = 12% p.a. = 12 ÷ 4 = 3% p.a.
• Time = 1year = 1 × 4 = 4years.

We will solve this question using simple interest method.

In this method we will find out the amount for four years and amount of fourth year will be final amount. After that we can easily find out compound interest by using formula.

Let's solve!

Amount for the first year

Principal = Rs. 8000

Rate = 3% p.a.

Time = 1year.

I = P × R × T/100

→ I = 8000 × 3 × 1/100

→ I = Rs . 240.

A = P + I

→ A = 8000 + 240

→ A = Rs. 8240.

Note - Amount of 1st year = Principal of 2nd year.

Amount for the second year

Principal = Rs. 8240.

Rate = 3% p.a.

Time = 1year.

I = P × R × T/100

→ I = 8240 × 3 × 1/100

→ I = Rs. 247.2.

A = P + I

→ A = 8240 + 247.2%

→ A = Rs. 8487.2.

Note - Amount of 2nd year = Principal of 3rd year.

Amount for the third year

Principal = Rs. 8487.2.

Rate = 3% p.a.

Time = 1year.

I = P × R × T/100

→ I = 8487.2 × 3 × 1/100

→ I = Rs. 254.616.

A = P + I

→ A = 8487.2 + 254.616

→ A = Rs. 8741.816.

Note - Amount of 3rd year = Principal of 4th year.

Amount(Final) for the fourth year

Principal = Rs. 8741.816.

Rate = 3% p.a.

Time = 1year.

I = P × R × T/100

→ I = 8741.816 × 3/100

→ I = Rs. 262.254

A = P + I

→ A = 8741.816 + 262.254

→ Final Amount = Rs. 9004.07.

Calculating Compound Interest

Final Amount = Rs. 9004.07.

Original Principal = Rs. 8000.

C.I. = Final Amount - Original Principal

→ C.I. = 9004.07 - 8000

→ C.I. = Rs. 1004.07.

Final Answer

• Compound Interest = Rs. 1004.07.

Used Abbreviations

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

______________________________

Answer 2

Given :

• Principal = Rs.8000
• Rate = 12 %
• Time = 1 year
• Compounded = Quarterly

$\\ \rule{200pt}{3pt}$

To Find :

• Compound Interest = ?

$\\ \rule{200pt}{3pt}$

Solution :

~ Formula Used :

• Amount :

${\pink{\dashrightarrow}} \; \; {\underline{\boxed{\color{darkblue}{\pmb{\sf{ Amount = Principal \bigg\{ 1 + \dfrac{Rate}{400} \bigg\}^{4 \times Time } }}}}}}$

• Compound Interest :

${\pink{\dashrightarrow}} \; \; {\underline{\boxed{\color{darkblue}{\pmb{\sf{ Compound \; Interest = Amount - Principal }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Amount :

${\longmapsto{\qquad{\sf{ Amount = Principal \bigg\{ 1 + \dfrac{Rate}{400} \bigg\}^{4 \times Time } }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 8000 \bigg\{ 1 + \dfrac{12}{400} \bigg\}^{4 \times 1 } }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 8000 \bigg\{ 1 + \dfrac{12}{400} \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 8000 \bigg\{ 1 + \cancel\dfrac{12}{400} \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 8000 \bigg\{ 1 + \cancel\dfrac{6}{200} \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 8000 \bigg\{ 1 + \cancel\dfrac{3}{100} \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 8000 \bigg\{ 1 + 0.03 \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 8000 \bigg\{ 1.03 \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 8000 \times 1.03 \times 1.03 \times 1.03 \times 1.03 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 8000 \times 1.12550881 }}}} \\ \\ \ {\qquad{\purple{\sf{ Amount = ₹ \; 9004.070 }}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Compound Interest :

${\implies{\qquad{\sf{ Compound \; Interest = Amount - Principal }}}} \\ \\ \ {\implies{\qquad{\sf{ Compound \; Interest = 9004.070 - 8000 }}}} \\ \\ \ {\qquad{\red{\sf{ Compound \; Interest = ₹ \; 1004.070 }}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Therefore :

❛❛ Compound Interest on this sum of money is ₹ 1004.070 . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$