What is compound interest on an amount of Rs 10000 at 8% per annum for 2 years?

What is the compound interest on a sum Rs. 10,000 at 12% per annum for 1 year and 4 months, when the interest is compounded at every 8 months?

1. Rs. 1,364
2. Rs. 1,664
3. Rs. 1,504
4. Rs. 1,264

Answer (Detailed Solution Below)

Option 2 : Rs. 1,664

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SSC GD Previous Paper 2 (Held On: 13 Feb 2019 Shift 1)_Hindi

100 Questions 100 Marks 90 Mins

Given:

Principal = Rs. 10,000

Rate of interest = 12%

Time = 1 year and 4 months = 16 months

Formula used:

A = P (1 + r/100)n

C.I = A - P

Where, A = Amount, P = Principal, n = Time, C.I = Compound interest

Calculation:

Interest is compounded on 8 months,

So, Time = 16/8 = 2 years

Rate of interest = 12% × (8/12)  = 8%

A = P (1 + r/100)n

⇒ Amount = 10,000 × (1 + 8/100)2

⇒ Amount = 10,000 × (108/100)2

⇒ Amount = (108)2

⇒ Amount = Rs. 11,664

C.I = A - P

⇒ C.I = 11,664 – 10,000

⇒ C.I = 1,664

∴ The compound interest is Rs. 1,664.

Alternate Method

Interest is compounded on every 8 months

So, Time = 16/8 = 2 years

Rate of interest = 12% × (8/12)  = 8% 

Effective rate formula for two years = (A + B + AB/100)

Here, A = B = 8%

⇒ Effective rate formula for two years = {8 + 8 + (64/100)} = 16.64%

⇒ Compound interest = 10,000 × 16.64%

⇒ Compound interest = Rs. 1664

∴ The compound interest is Rs. 1,664.

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Find the compound interest on a sum of Rs. 10000 if invested at the rate of 15% per annum for 2 years.

1. 3225
2. 13225
3. 225
4. 1250

Answer (Detailed Solution Below)

Option 1 : 3225

Given:

Principal = Rs. 10000

Time = 2 years

Rate of interest = 15% per annum

Formula used:

A = P{1 + (r/100)}n

C.I = A - P

Where, A is amount, C.I is compound Interest, P is principle, r is rate of interest and n is time.

Calculation:

A = 10000{(1 + (15/100)}2

⇒ A = 10000(115/100)2 

⇒ A = 10000 × (23/20) × (23/20)

⇒ A = 13225.

According to the question,

⇒ C.I. = 13225 - 10000

⇒ C.I. = Rs. 3225

∴ The compound interest is Rs. 3225.

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For 1st year Principal(P) =Rs. 10000, Rate(R) =8% Time(T) =1 year ∴ Interest = 10000×8×1100=100×8=Rs.800 For 2nd year P= Rs. 10000 +Rs. 800=Rs. 10800 Rate(R) =8% Time(T)=1 year ∴ Interest= 10800×8×1100=108×8=Rs.864 For 3rd year ∴ P= Rs. 10800 +Rs. 864 =Rs. 11664, R=8%, T=1 year ∴ Interest= 11664×8×1100=11664×225 =Rs. 933.12 ∴ Amount =Rs. 11664 +933.12 =Rs. 12597.12 Hence required amount =Rs. 12597.12 ∴ Compound interest =Rs. 12597.12 -10000=Rs. 2597.12

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