Compound Interest
- The simple interest on a certain sum of money for 2 years at 5% is Rs. 1600. The compound interest at the same rate after 3 years interest compound annually, is
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As we know that ,
Principal = S.I. × 100 Time × Rate Principal = 1600 × 100 = Rs. 16000 5 × 2 C.I. = P 
1 + R 
T − 1 
100 C.I. = 16000 1 + 5 3 − 1 100 C.I. = 16000 21 3 − 1 20
Correct Option: B
As we know that ,
Principal = S.I. × 100 Time × Rate Principal = 1600 × 100 = Rs. 16000 5 × 2 C.I. = P 1 + R T − 1 100 C.I. = 16000 1 + 5 3 − 1 100 C.I. = 16000 21 3 − 1 20 C.I. = 16000 
9261 − 1 8000 C.I. = 16000 × 1261 = Rs. 2522 8000
- The simple interest on a sum of money for 3 years is Rs. 240 and the compound interest on the same sum, at the same rate for 2 years is Rs. 170. The rate of interest is :
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As per the given in question ,
∵ S.I. for 3 years = Rs. 240∴ S.I. for 2 years = 240 × 2 = Rs. 160 3 ∴ SI = P × R × T 100 ∴ PR × 2 = 160 100
⇒ PR = 160 × 50 = 8000...(i)
Again, C.I. – S.I. = 170 – 160 = Rs. 10⇒ Difference = PR2 10000 ⇒ PR2 = 10 10000
Correct Option: C
As per the given in question ,
∵ S.I. for 3 years = Rs. 240∴ S.I. for 2 years = 240 × 2 = Rs. 160 3 ∴ SI = P × R × T 100 ∴ PR × 2 = 160 100
⇒ PR = 160 × 50 = 8000...(i)
Again, C.I. – S.I. = 170 – 160 = Rs. 10⇒ Difference = PR2 10000 ⇒ PR2 = 10 10000 ⇒ 8000 × R = 10 10000 ⇒ R = 100 = 25 = 12 1 % 8 2 2
- On a certain sum of money, the simple interest for 2 years is Rs. 350 at the rate of 4% per annum. If it was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned ?
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Time = 2 year , Rate = 4% , S.I. = Rs. 350
As we know that ,Principal = S.I. × 100 Time × Rate Principal = 350 × 100 = Rs. 4375 2 × 4 Difference = PR2 10000
Correct Option: B
Time = 2 year , Rate = 4% , S.I. = Rs. 350
As we know that ,Principal = S.I. × 100 Time × Rate Principal = 350 × 100 = Rs. 4375 2 × 4 Difference = PR2 10000 Difference = 4375 × 4 × 4 = Rs. 7 10000
- A certain amount of money earns Rs. 540 as Simple Interest in 3 years. If it earns a Compound Interest of Rs. 376.20 at the same rate of interest in 2 years, find the amount (in Rupees).
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Given in question , S.I. for 3 years = Rs. 540
S.I. for 2 years = 2 × 540 = Rs. 360 3
C.I. for 2 years = Rs. 376.20
C.I. – S.I. = 376.20 – 360 = Rs. 16.20
We have , S.I. for 1 year = Rs. 180∴ Rate of interest = 16.20 × 100 = 9% per annum 180 ∴ Principal = S.I. × 100 Time × Rate
Correct Option: C
Given in question , S.I. for 3 years = Rs. 540
S.I. for 2 years = 2 × 540 = Rs. 360 3
C.I. for 2 years = Rs. 376.20
C.I. – S.I. = 376.20 – 360 = Rs. 16.20
We have , S.I. for 1 year = Rs. 180∴ Rate of interest = 16.20 × 100 = 9% per annum 180 ∴ Principal = S.I. × 100 Time × Rate
Here , Time = 1 year , Rate = 9%Principal = 180 × 100 = Rs. 2000 1 × 9
- A man borrowed some money from a private organisation at 5% simple interest per annum. He lended 50% of this money to another person at 10% compound interest per annum and thereby the man made a profit of Rs. 3,205 in 4 years. The man borrowed.
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Suppose Sum borrowed = Rs. P
Given that , Rate ( R ) = 5% , Time = 4 years∴ Simple interest after 4 years ( SI ) = P × 4 × 5 = Rs. P 100 5 Amount lent of on compound interest = Rs. x 2 ∴ C.I. = P 1 + R T − 1 100 C.I. = P 1 + 10 4 − 1 2 100 C.I. = P [(1.1)4 − 1] 2 C.I. = P (1.4641 − 1) 2 C.I. = Rs. 0.4641P 2
∴ C.I. - S.I. = 3205
Correct Option: B
Suppose Sum borrowed = Rs. P
Given that , Rate ( R ) = 5% , Time = 4 years∴ Simple interest after 4 years ( SI ) = P × 4 × 5 = Rs. P 100 5 Amount lent of on compound interest = Rs. x 2 ∴ C.I. = P 1 + R T − 1 100 C.I. = P 1 + 10 4 − 1 2 100 C.I. = P [(1.1)4 − 1] 2 C.I. = P (1.4641 − 1) 2 C.I. = Rs. 0.4641P 2
∴ C.I. - S.I. = 3205∴ 0.4641P − P = 3205 2 5 ⇒ 2.3205P − 2P = 3205 10
⇒ 0.3205P = 32050⇒ P = 32050 = Rs. 100000 0.3205
