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?
- Rs. 1,364
- Rs. 1,664
- Rs. 1,504
- 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.
- 3225
- 13225
- 225
- 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