Question

*What is the compound interest on Rs. 200 for 1 year at 10% rate compounded half-yearly*

1️⃣ Rs.200
2️⃣ Rs.220.50
3️⃣ Rs. 320.50
4️⃣ Rs. 100.50​

Answer 1

$\underline{ \underline{ \tt{REQUIRED \: ANSWER -}}}$

Principal = ₹200

Time = 1 year compounded half yearly

Rate = 10%

Now,

For 1st ½ year,

P = ₹200

R = 10%

T = ½ year

$\: \: \: \: \: \underline{ \boxed{ \tt{ \gray{Interest = \dfrac{P × R × T}{100} } }}} \\ \\ \tt{ = ₹ \: \frac{ \cancel{2 }\cancel{0} \cancel{0} \times 10 \times 1}{1 \cancel{0} \cancel{0} \times \cancel{2}} } \\ \\ \tt{ = ₹ \: 10} \\ \\ \\ \underline{ \boxed{ \gray{ \tt{Amount = P + I}}}} \\ \\ \tt{ = ₹ \: 200 + 10 } \\ \tt{ = ₹ \: 210}$

For 2nd ½ year,

P = ₹210

R = 10%

T = ½ year

$\tt{Interest = ₹ \: \dfrac{21 \cancel0 \times 1 \cancel0 \times 1}{1 \cancel0 \cancel0 \times 2} } \\ \\ \tt{ = ₹ \: \frac{21}{2} } \\ \\ \tt{ = ₹ \: 1.5} \\ \\ \\ \tt{Amount =₹ \: 210 + ₹1.5} \\ \tt{ =₹ \: 211.5 }$

Now,

Required amount = ₹ 211.5

$\underline{ \boxed{ \gray{ \tt{C.I = required \: amount - Initial \: Principal}}}} \\ \\ \tt{ = ₹ \: 211.5 - ₹ \: 200} \\ \boxed{ \green{ \tt{ = ₹ \:11.5 \: \: \: ans.. }}}$

______________________

@MissSolitary ✌️

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Answer 2

Given :-

• Principal = Rs.200
• Time = 1 year.
• Rate = 10% compounded half-yearly .

To Find :-

• Compound interest = ?

Solution :-

we know that, when rate is compounded half - yearly,

• Time = 2 times = 1 * 2 = 2 years.
• Rate = Half = 10 / 2 = 5% per annum .
• Amount = P[1 + (R/100)]^(time)
• CI = Amount - Principal .

putting values we get,

→ A = 200[1 + (5/100)]²

→ A = 200 * [1 + (1/20)]²

→ A = 200 * (21/20)²

→ A = (200 * 441)/400

→ A = (441/2)

→ A = Rs.220.5 .

therefore,

→ CI = A - P

→ CI = 220.5 - 200

→ CI = Rs.20.5 (Ans.)

Hence, Amount after 1 year is Rs.220.5 and compound interest recieved is Rs.20.5 .

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