Compound Interest
- Find the rate percent per annum, if Rs. 2000 amounts to Rs. 2,315.25 in a year and a half,
interest being compounded half yearly.
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As per the given in question ,
Time = 3 years = 3 half years 2
Rate = 2R% per annum = R% per half year∴ Amount = Principal – 
1 + Rate 
Time 100 ⇒ 2315.25 = 2000 1 + R 3 100 ⇒ 231525 = 1 + R 3 200000 100 ⇒ 9261 = 1 + R 3 8000 100 ⇒ 21 3 = 1 + R 3 20 100 ⇒ 1 + 1 3 = 1 + R 3 20 100
Correct Option: B
As per the given in question ,
Time = 3 years = 3 half years 2
Rate = 2R% per annum = R% per half year∴ Amount = Principal – 1 + Rate Time 100 ⇒ 2315.25 = 2000 1 + R 3 100 ⇒ 231525 = 1 + R 3 200000 100 ⇒ 9261 = 1 + R 3 8000 100 ⇒ 21 3 = 1 + R 3 20 100 ⇒ 1 + 1 3 = 1 + R 3 20 100 ⇒ 1 + 1 = 1 + R 20 100 ⇒ R = 1 100 20 ⇒ R = 100 = 5% per half year 20
∴ Required rate = 10% per annum
- A man gave 50% of his savings of ₹ 84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was
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Amount given to sons = 84100 × 1 = ₹ 42050 2
Let Amount given to B = ₹ y
∴ Amount given to A = ₹ (42050 – y)A = P 1 + R T 100 ⇒ (42050 – y ) 1 + R 3 = y 1 + R 5 100 100 ⇒ (42050 – y ) = y 1 + R 2 100 ⇒ (42050 – y ) = y 1 + 5 2 100 ⇒ (42050 – y ) = y 1 + 1 2 20 ⇒ 42050 – y = y 21 2 20 ⇒ 42050 – y = 441y 400
Correct Option: A
Amount given to sons = 84100 × 1 = ₹ 42050 2
Let Amount given to B = ₹ y
∴ Amount given to A = ₹ (42050 – y)A = P 1 + R T 100 ⇒ (42050 – y ) 1 + R 3 = y 1 + R 5 100 100 ⇒ (42050 – y ) = y 1 + R 2 100 ⇒ (42050 – y ) = y 1 + 5 2 100 ⇒ (42050 – y ) = y 1 + 1 2 20 ⇒ 42050 – y = y 21 2 20 ⇒ 42050 – y = 441y 400 ⇒ 42050 = 441y + y 400 ⇒ 42050 = 441y + 400y 400 ⇒ 42050 = 841y 400
⇒ 841 y = 42050 × 400⇒ y = 42050 × 400 = ₹ 20,000 841
- What does ₹ 250 amounts to in 2 years with compound interest at the rate of 4% in the 1st year and 8% in the second year ?
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Here , P = ₹ 250 , R1 = 4% , R2 = 8%
A = P 1 + R1 T1 1 + R2 T2 100 100 A = 250 1 + 4 1 + 8 100 100
Correct Option: B
Here , P = ₹ 250 , R1 = 4% , R2 = 8%
A = P 1 + R1 T1 1 + R2 T2 100 100 A = 250 1 + 4 1 + 8 100 100 A = 250 × 104 × 108 100 100
∴ A = ₹ 280.80
- Sita deposited ₹ 5,000 at 10% simple interest for 2 years. How much more money will Sita have in her account at the end of two years, if it is compounded semiannually.
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Given in question , Rate = 5%, Time = 4 half years , P = ₹ 5000
∴ C.I. = P 
1 + R T − 1 
100 C.I. = 5000 1 + 5 4 − 1 100 C.I. = 5000 194481 − 1 160000 C.I. = 5000 × 34481 = ₹ 1077.5 160000
Correct Option: C
Given in question , Rate = 5%, Time = 4 half years , P = ₹ 5000
∴ C.I. = P 1 + R T − 1 100 C.I. = 5000 1 + 5 4 − 1 100 C.I. = 5000 194481 − 1 160000 C.I. = 5000 × 34481 = ₹ 1077.5 160000 S.I.= 5000 × 10 × 2 = ₹ 1000 100
Required Difference = C.I. - S.I.
Difference = 1077.5 – 1000 = ₹ 77.5
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and paid back in two years in two equal annual instalments. What was the amount of each instalment ?A sum of 13,360 was borrowed at 8 3 % per annum compound interest 4
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Let each instalment be y.
y + y = 13360 1 + 35 
2 1 + 35 400 400 ⇒ y + y = 13360 1 + 7 2 1 + 7 80 80 ⇒ 6400y + 80y = 13360 7569 87
Correct Option: B
Let each instalment be y.
y + y = 13360 1 + 35 2 1 + 35 400 400 ⇒ y + y = 13360 1 + 7 2 1 + 7 80 80 ⇒ 6400y + 80y = 13360 7569 87 ⇒ 6400y + 6960y = 13360 7569
⇒ 13360 y = 13360 × 7569
⇒ y = ₹ 7569
