Compound Interest
- The difference between the compound and the simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually, is ₹ 28. If the interest were compounded halfyearly, the difference in the two interests will be
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Given that , Difference = C.I. - S.I. = ₹ 28 , Time = 2 years , Rate = 10%
If the difference between compound interest and simple interest at the rate of r% per annum for 2 years be ( C.I. - S.I. ) , thenPrincipal = ( C.I. - S.I. ) 
100 
2 r Principal = 28 100 2 = ₹ 2800 10
If the interest is compounded half yearly, then⇒ r = 10 = 5% , Time = 4 half years 2 ∴ Simple interest = P × R × T 100 Simple interest = 2800 × 5 × 4 = ₹ 560 100
Correct Option: C
Given that , Difference = C.I. - S.I. = ₹ 28 , Time = 2 years , Rate = 10%
If the difference between compound interest and simple interest at the rate of r% per annum for 2 years be ( C.I. - S.I. ) , thenPrincipal = ( C.I. - S.I. ) 100 2 r Principal = 28 100 2 = ₹ 2800 10
If the interest is compounded half yearly, then⇒ r = 10 = 5% , Time = 4 half years 2 ∴ Simple interest = P × R × T 100 Simple interest = 2800 × 5 × 4 = ₹ 560 100 Compound interest = 2800 
1 + 5 4 − 1 
100
Compound interest = 2800 [1.2155 – 1]
Compound interest = 2800 × 0.2155 = 603.41
∴ Difference = Compound interest - Simple interest
∴ Difference = ₹ (603.41 – 560) = ₹ 43.41
- The amount on Rs. 25,000 in 2 years at annual compound interest, if the rates for the successive years be 4% and 5% per annum respectively is :
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Given that , Principal = Rs. 25,000 , Time = 2 years , R1 = 4% , R2 = 5%
Using the given formula ,Amount = P 1 + R1 1 + R2 100 100 Amount = 25000 1 + 4 1 + 5 100 100
Correct Option: C
Given that , Principal = Rs. 25,000 , Time = 2 years , R1 = 4% , R2 = 5%
Using the given formula ,Amount = P 1 + R1 1 + R2 100 100 Amount = 25000 1 + 4 1 + 5 100 100 Amount = 25000 × 104 × 105 100 100
Amount = Rs. 27300
- The simple interest on a certain sum for 2 years is ₹ 50 and the compound interest is ₹ 55. Find the rate of interest per annum and the sum.
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Here , CI = ₹ 55 , SI = ₹ 50
The difference between CI and SI for 2 years period is because CI also includes interest for the second year on the first year’s interest.
CI – SI = ₹ (55 – 50) = ₹ 5First year’s SI = 50 = ₹ 25 2
So, ₹ 5 is the interest on ₹ 25 for 1 year.r = 100 × I P × t
Here, I = ₹ 5 , P = ₹ 25 , t = 1 year∴ r = 100 × 5 25 × 1
r = 20% per annum.Now, P = 100 × I r × t
Here, SI = ₹ 50 , r = 20% per annum , t = 2 years.
Correct Option: C
Here , CI = ₹ 55 , SI = ₹ 50
The difference between CI and SI for 2 years period is because CI also includes interest for the second year on the first year’s interest.
CI – SI = ₹ (55 – 50) = ₹ 5First year’s SI = 50 = ₹ 25 2
So, ₹ 5 is the interest on ₹ 25 for 1 year.r = 100 × I P × t
Here, I = ₹ 5 , P = ₹ 25 , t = 1 year∴ r = 100 × 5 25 × 1
r = 20% per annum.Now, P = 100 × I r × t
Here, SI = ₹ 50 , r = 20% per annum , t = 2 years.P = 100 × 50 20 × 2
P = ₹ 125.
Note : Derivation for 2 years problems :
We can find required answer with the help of given formula ,Rate = 2 × (CI − SI) × 100 SI Sum = SI × 100 Rate × 2
- The compound interest on a sum of money at 5% per annum for 3 years is ₹ 2522. What would be the simple interest on this sum at the same rate and for the same period ?
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Given that , CI = ₹ 2522 , r = 5% , t = 3 years
We can find required answer with the help of given formula ,SI = CI × rt 100 1 + r t − 1 100 SI = 2522 × 5 × 3 100 1 + 5 3 − 1 100
Correct Option: B
Given that , CI = ₹ 2522 , r = 5% , t = 3 years
We can find required answer with the help of given formula ,SI = CI × rt 100 1 + r t − 1 100 SI = 2522 × 5 × 3 100 1 + 5 3 − 1 100 SI = 2522 × 5 × 3 100 9261 − 1 8000 ∴ SI = 2522 × 5 × 3 × 8000 = ₹ 2400. 100 × 1261
- If SI on a certain sum of money at 4% per annum for 2 years be ₹ 125, what would be the interest if it was to be compounded annually at the same rate and for the same time period?
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Given in question , SI = ₹ 125 , r = 4% , t = 2 years
Using the given formula ,
CI = 100 × 51 125 4 × 2 × 625
Correct Option: A
Given in question , SI = ₹ 125 , r = 4% , t = 2 years
Using the given formula ,CI = 100 × 51 125 4 × 2 × 625 CI = 100 × 51 × 125 = ₹ 127.5. 4 × 2 × 625
