Find the amount and compound interest on ₹ 64000 for 1 year at 8 per annum compounded half yearly

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Solution : Principal`=`Rs `64000`<br>Time`=1` year<br>Rate`=10%`<br>`=64000(1+ 1/4)^4 `<br>` =64000(1.025)^4 `<br>` =64000×1.10381`<br>` =70644.025`<br>Amount is Rs `70644.025`

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Find the compound interest on Rs 64000 for 1 year at the rate of 10% per annum compounded quarterly.

Solution

To calculate the interest compounded quarterly, we have: 
\[A = P \left( 1 + \frac{R}{400} \right)^{4n} \]
\[ = 64, 000 \left( 1 + \frac{10}{400} \right)^{4 \times 1} \]
\[ = 64, 000 \left( 1 . 025 \right)^4 \]
 = 70, 644 . 03
Thus, the required amount is Rs 70, 644 . 03.
Now, 
CI = A - P
 = Rs 70, 644 . 025 - Rs 64, 000
 = Rs 6, 644 . 03

The compound interest on a sum of Rs. 64000 at 5% per annum for a certain period is Rs. 4921, while the interest is compounded half-yearly. What will be the compound interest on the same sum at the same rate for the same period, if the interest is compounded annually?

1. Rs. 4890
2. Rs. 4880
3. Rs. 4820
4. Rs. 4860

Answer (Detailed Solution Below)

Option 2 : Rs. 4880

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Given:

Principal = Rs. 64000

Compound Interest = Rs. 4921

Rate = 5%

Concept used:

When the sum is compounded half-yearly, then the rate of interest becomes half and time becomes double.

Formula used:

A = P(1 + R/100)T

C.I = A - P

A = P + C.I

Where, A = Amount, P = Principal, T = Time, C.I = Compound interest and R = rate of interest

Calculation:

A = P + C.I

⇒ A = 64000 + 4921 = Rs. 68921

According to the question,

Compounded half-yearly,

A = P(1 + R/100)T

⇒ 68921 = 64000[1 + 5/(2 ×100)]2T

⇒ 68921/64000 = (41/40)2n

⇒ (41/40)3 = (41/40)2n

⇒ 2n = 3

⇒ n = 3/2

Annual

Now, compounded annually

P = Rs. 64000 n = 3/2 = \({1\frac{1}{2}}\) years, and r = 5%

A = P(1 + R/100)T

⇒ A = 64000(1 + 5/100)\({1\frac{1}{2}}\)

⇒ A = 64000(1 + 5/100)1 × (1 + 5/100)1/2

⇒ A = 64000 × (1 + 5/100)(1 + 5/2 × 100)

⇒ A = 64000 × 21/20 × 41/40 = Rs. 688,80

C.I = A - P

⇒ C.I = 68880 - 64000 = Rs. 4880

∴ The compound interest is Rs. 4880.

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