What will be the compound interest on ₹ 8000 at 20% per annum for 9 months compounded quarterly?

Find the compound interest on Rs. 8000 for 9 months @ 12% p.a., when interest is compounded quarterly.

1. 741.81
2. 898.91
3. 841.81
4. 899.91

Answer (Detailed Solution Below)

Option 1 : 741.81

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CT 1: Growth and Development - 1

10 Questions 10 Marks 10 Mins

Given:

Principal = Rs. 8000

Time = 9 Months

Rate of interest = 12% p.a.

Formula Used:

Compound interest = Principal × (1 + Rate%/100)Time - Principal

Calculation:

Interest is compounded quarterly, So

Time = 9/3 = 3

Rate of interest = 12%/4 = 3% p.a.

Compound interest = Principal × (1 + Rate%/100)Time - Principal

⇒ Compound interest = 8000 × (1 + 3/100)3 - 8000

⇒ Compound interest = 8741.81 - 8000

⇒ Compound interest = Rs. 741.81

∴ Compound interest is Rs. 741.81

The correct option is 1 i.e. Rs. 741.81

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9

Find the compound interest on Rs. 8000 for 9 months at 20% per annum compounded quarterly.

Principal = Rs.8000

Time =9 months

Rate = 20% per annum

∵ Interest is compounded quarterly, So Rate of interest will be counted as 20/4 = 5% and time will be 9/3 = 3 Quarter

We know that,

Hence, Compound Interest = Rs. 9261 – Rs 8000 = Rs. 1261

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Text Solution

Solution : `p=8000`<br>`T=9`months `=3` quarter<br>`R=20%=5%`quarter<br>`CI = p (1+R/100)t -p`<br>`=8000(1+5/100)3 -` Rs `8000`<br>`= 8000× 21/20×21/20×21/20-`Rs `8000`<br>`=9261-8000`<br>`=1261`

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Find the compound interest on Rs 8000 for 9 months at 20% per annum compounded quarterly.

Solution

P = Rs 8, 000
T = 9 months = 3 quarters
R = 20 % per annum = 5 % per quarter
\[A = 8, 000 \left( 1 + \frac{5}{100} \right)^3 \]
\[ = 8, 000 \left( 1 . 05 \right)^3 \]
 = 9, 261
The required amount is Rs 9, 261.
Now, 
CI = A - P
= Rs 9, 261 - Rs 8, 000
= Rs 1, 261

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