Compound Interest
- The compound interest on a certain sum of money at a certain rate for 2 years is 40.80 and the simple interest on the same sum is 40 at the same rate and for the same time. The rate of interest is
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Here , Compound Interest ( CI ) = ₹ 40.80 , Simple Interest ( SI ) = ₹ 40
Let the principal be P and rate of interest be r percent per annum. Then,C.I. = P 
1 + r 
2 − 1 
100 ⇒ 40.80 = P 1 + r 2 − 1 ....(i) 100 S.I. = P.r.t ⇒ 40 = Pr × 2 ...(ii) 100 100 
⇒ 1.02 = 100 1 + r2 + 2r − 1 2r 10000 100 ⇒ 1.02 = r + 1 200 ⇒ r = 1.02 − 1 200
⇒ r = 0.02 × 200
∴ r = 4% per annum.
We can find required answer with the help of given formula :
Here, C.I. = ₹ 40.80 , S.I. = ₹ 40 , R = ?C.I.= S.I. 
1 + R 200
Correct Option: C
Here , Compound Interest ( CI ) = ₹ 40.80 , Simple Interest ( SI ) = ₹ 40
Let the principal be P and rate of interest be r percent per annum. Then,C.I. = P 1 + r 2 − 1 100 ⇒ 40.80 = P 1 + r 2 − 1 ....(i) 100 S.I. = P.r.t ⇒ 40 = Pr × 2 ...(ii) 100 100 ⇒ 1.02 = 100 1 + r2 + 2r − 1 2r 10000 100 ⇒ 1.02 = r + 1 200 ⇒ r = 1.02 − 1 200
⇒ r = 0.02 × 200
∴ r = 4% per annum.
We can find required answer with the help of given formula :
Here, C.I. = ₹ 40.80 , S.I. = ₹ 40 , R = ?C.I.= S.I. 1 + R 200 40.80 = 40 1 + R 200 4080 = 1 + R 4000 200 408 = 200 + R 400 200
⇒ 408 = 400 + 2R
⇒ 2R = 8 ⇒ R = 4%
Hence , Rate = 4%
- The compound interest on a certain sum of money invested for 2 years at 5% per annum is ₹ 328. The simple interest on the sum, at the same rate and for the same period will be
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Given that , Compound Interest ( CI ) = ₹ 328 , Rate ( R ) = 5% , Time = 2 years
Let the principal be P.∴ C.I. = P 1 + R T − 1 100 ⇒ 328 = P 1 + 5 2 − 1 100 ⇒ 328 = P 441 − 1 400 ⇒ 328 = P 441 − 400 400 ⇒ P = 328 × 400 = ₹ 3200 41 ∴ S.I. = PRT = 3200 × 5 × 2 = ₹ 320 100 100
Second Method to solve this question :
Here, C.I. = ₹ 328 , R = 5% , S.I. = ?C.I.= S.I. 1 + R 200
Correct Option: A
Given that , Compound Interest ( CI ) = ₹ 328 , Rate ( R ) = 5% , Time = 2 years
Let the principal be P.∴ C.I. = P 1 + R T − 1 100 ⇒ 328 = P 1 + 5 2 − 1 100 ⇒ 328 = P 441 − 1 400 ⇒ 328 = P 441 − 400 400 ⇒ P = 328 × 400 = ₹ 3200 41 ∴ S.I. = PRT = 3200 × 5 × 2 = ₹ 320 100 100
Second Method to solve this question :
Here, C.I. = ₹ 328 , R = 5% , S.I. = ?C.I.= S.I. 1 + R 200 328 = S.I. 1 + 5 200 328 = S.I. 1 + 1 40 S.I. = 328 × 40 41
S.I. = 8 x 40 = ₹ 320
- Compound interest on a sum of money for 2 years at 4 percent per annum is ₹ 2, 448. Simple interest of the same sum of money at the same rate of interest for 2 years will be
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Given that , Compound Interest ( CI ) = ₹ 2, 448 , Rate ( R ) = 4% , Time = 2 years
Using the given formula ,C.I.= P 1 + r t − P 100 2448 = P 1 + 4 t − 1 100 ⇒ 2448 = P 1 + 4 2 − 1 100 ⇒ 2448 = P 676 − 1 625 ⇒ 2448 = P 676 - 625 625 ⇒ 2448 = P 51 625 ∴ P = 2448 × 625 = ₹ 30,000 51 ∴ S.I. = 30000 × 4 × 2 = ₹ 2400 100
We can find required answer with the help of given formula :
Here, C.I. = ₹ 2448 , R = 4% , S.I. = ?C.I. = S.I. 1 + R 200 2448 = S.I. 1 + 4 200
Correct Option: B
Given that , Compound Interest ( CI ) = ₹ 2, 448 , Rate ( R ) = 4% , Time = 2 years
Using the given formula ,C.I.= P 1 + r t − P 100 2448 = P 1 + 4 t − 1 100 ⇒ 2448 = P 1 + 4 2 − 1 100 ⇒ 2448 = P 676 − 1 625 ⇒ 2448 = P 676 - 625 625 ⇒ 2448 = P 51 625 ∴ P = 2448 × 625 = ₹ 30,000 51 ∴ S.I. = 30000 × 4 × 2 = ₹ 2400 100
We can find required answer with the help of given formula :
Here, C.I. = ₹ 2448 , R = 4% , S.I. = ?C.I. = S.I. 1 + R 200 2448 = S.I. 1 + 4 200 2448 = S.I. 1 + 1 50 2448 = S.I. 51 50 S.I. = 2448 × 50 = ₹ 2400 51
- At a certain rate per annum, the simple interest on a sum of money for one year is ₹ 260 and the compound interest on the same sum for two years is ₹ 540.80. The rate of interest per annum is
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Here , Simple interest for 1 year = ₹ 260 , Compound interest for 2 year = ₹ 540.80
Let the principal be P and rate of interest be r% per annum.Now, S.I. = Principal × Time × Rate 100 260 = P × r × 1 ....(i) 100 C.I.= P 1 + R T − 1 100 540.80 = P 1 + r 2 − 1 100 ⇒ 540.80 = P 1 + 2r + r2 − 1 100 10000
Correct Option: C
Here , Simple interest for 1 year = ₹ 260 , Compound interest for 2 year = ₹ 540.80
Let the principal be P and rate of interest be r% per annum.Now, S.I. = Principal × Time × Rate 100 260 = P × r × 1 ....(i) 100 C.I.= P 1 + R T − 1 100 540.80 = P 1 + r 2 − 1 100 ⇒ 540.80 = P 1 + 2r + r2 − 1 100 10000 ⇒ 540.80 = 2Pr + Pr2 100 10000 ⇒ 540.80 = 2 × 260 + 260.r 100
⇒ 260r = 54080 – 52000
⇒ 260r = 2080⇒ r = 2080 = 8% 260
- The simple interest on a sum of money at 4% per annum for 2 years is ₹ 80. The compound interest in the same sum for the same period is
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Given that , S.I. = ₹ 80 , Time = 2 years , Rate = 4%
We know that ,Principal = S.I. × 100 Time × Rate Principal = 80 × 100 = 1000 2 × 4 ∴ C.I. = P 1 + R T − 1 100 C.I. = 1000 1 + 4 2 − 1 100 C.I. = 1000 26 2 − 1 25 C.I. = 1000 676 − 1 625 C.I. = 1000 676 − 625 625 C.I. = 1000 × 51 = ₹ 81.60 625
We can find required answer with the help of given formula :
Here, S.I. = ₹ 80, R = 4%, C.I. = ?C.I. = S.I. 1 + R 200
Correct Option: D
Given that , S.I. = ₹ 80 , Time = 2 years , Rate = 4%
We know that ,Principal = S.I. × 100 Time × Rate Principal = 80 × 100 = 1000 2 × 4 ∴ C.I. = P 1 + R T − 1 100 C.I. = 1000 1 + 4 2 − 1 100 C.I. = 1000 26 2 − 1 25 C.I. = 1000 676 − 1 625 C.I. = 1000 676 − 625 625 C.I. = 1000 × 51 = ₹ 81.60 625
We can find required answer with the help of given formula :
Here, S.I. = ₹ 80, R = 4%, C.I. = ?C.I. = S.I. 1 + R 200 C.I. = 80 1 + 4 200 C.I. = 80 1 + 1 50 C.I. = 80 × 51 = ₹ 81.60 50
