Compound Interest
- A moneylender lends Rs. 2000 for 6 months at 20% per annum whereas the interest is compounded quarterly. After the given period he will get the amount of ?
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For the quarterly interest,
Time = (6/12) year x 4 = 2 quarterly
Rate = 20/4 = 5%
(∴ On quarterly interest time is multiplied by 4 and rate is divided by 4)
Hence,required amount = Principal (1 + Rate/100)TimeCorrect Option: A
For the quarterly interest,
Time = (6/12) year x 4 = 2 quarterly
Rate = 20/4 = 5%
(∴ On quarterly interest time is multiplied by 4 and rate is divided by 4)
Hence,required amount = Principal (1 + Rate/100)Time
= 2000(1 +5/10)2
= 2000(21/20)2
= Rs. 2205
- In what time will Rs. 6250 amount to Rs. 6632.55 at 4% compound interest payable half yearly ?
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Since Interest accumulates half yearly so effective rate = R/2 = 4/2 = 2.
And effective time is 2t.
∵ 6250 [1 + 2/100]2t = 6632.55Correct Option: B
Since Interest accumulates half yearly so effective rate = R/2 = 4/2 = 2.
And effective time is 2t.
∵ 6250 [1 + 2/100]2t = 6632.55
⇒ (1 +2/100)2t = 663255/625000 = 132651/125000 = (51/50)3
⇒ (51/50)2t = (51/50)3
⇒ 2t =3
∴ t = 3/2 years
- Find the effective annual rate of 4 per cent per annum compound interest paid quarterly.?
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Effective annual rate = 100(1 + {(4/4) /100})4 - 100
= (101/100)4 x 100 - 100Correct Option: A
Effective annual rate = 100(1 + {(4/4) /100})4 - 100
= (101/100)4 x 100 - 100
= 104.0604 - 100
= 4.0604%
- In what time will Rs. 390625 amount to Rs. 456976 at 4 per cent compound interest ?
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∵ P(1 + r/100)t = A
⇒ 390625(1 + 4/100)t = 456976Correct Option: B
∵ P(1 + r/100)t = A
⇒ 390625(1 + 4/100)t = 456976
⇒ (1 + 4/100)t = 456976/390625 =(26/25)4
⇒ (26/25)t = (26/25)4
⇒ t = 4
∴ The required time is 4 years.
- The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is Rs. 1.50. The sum is ?
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Let the sum be Rs . 100 then
S.I. = Rs.(100 x 5 x 2/100)= Rs. 10
C.I = Rs. [{100 x (1 + 5/100)2} - 100] = Rs. 41/4
∴ Difference between C.I and S.I = Rs. (41/4 - 10) = Re. 0.25
⇒ 0.25 : 150 : : 100 : P
∴ P = (1.50 x 100) / 0.25 = Rs. 600Correct Option: A
Let the sum be Rs . 100 then
S.I. = Rs.(100 x 5 x 2/100)= Rs. 10
C.I = Rs. [{100 x (1 + 5/100)2} - 100] = Rs. 41/4
∴ Difference between C.I and S.I = Rs. (41/4 - 10) = Re. 0.25
⇒ 0.25 : 150 : : 100 : P
∴ P = (1.50 x 100) / 0.25 = Rs. 600
