Compound Interest
- The time in which ₹ 80,000 amounts to ₹ 92,610 at 10% p.a. compound interest, interest being compounded semi annually is :
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Given Here , Amount ( A ) = ₹ 92,610 , P = ₹ 80,000 , Rate ( R ) = 10% p.a. , Time = t half year and R = 5% per half year
∴ A = P 
1 + R 
T 100 ⇒ 92,610 = 80,000 1 + 5 T 100 ⇒ 92610 = 1 + 5 T 80000 100 ⇒ 9261 = 21 T 8000 20
Correct Option: A
Given Here , Amount ( A ) = ₹ 92,610 , P = ₹ 80,000 , Rate ( R ) = 10% p.a. , Time = t half year and R = 5% per half year
∴ A = P 1 + R T 100 ⇒ 92,610 = 80,000 1 + 5 T 100 ⇒ 92610 = 1 + 5 T 80000 100 ⇒ 9261 = 21 T 8000 20 ⇒ 21 3 = 21 T 20 20 ⇒ T = 3 half years or 1 1 years 2
- A man saves ₹ 2000 at the end of each year and invests the money at 5% compound interest. At the end of 3 years he will have :
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As per the given question,
Amount = 2000 1 + 5 2 + 2000 1 + 5 100 100 Amount = 2000 × 21 2 + 2000 21 20 20
Correct Option: B
As per the given question,
Amount = 2000 1 + 5 2 + 2000 1 + 5 100 100 Amount = 2000 × 21 2 + 2000 21 20 20 ⇒ Amount = 2000 × 21 × 41 = ₹ 4305 20 20
∴ Required amount = 4305 + 2000 = ₹ 6305
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interest being compounded semi-annually is :The compound interest on Rs. 24000 at 10% per annum for 1 1 years, 2
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Here , P = Rs. 24000 , Rate = 10% per annum = 5% per half year
Time = 1 1 years = 3 half years 2 ∴ C.I. = P 
1 + R T − 1 
100 C.I. = 24000 1 + 5 3 − 1 100 C.I. = 24000 1 + 1 3 − 1 20 C.I. = 24000 21 3 − 1 20 C.I. = 24000 
9261 − 1 8000
Correct Option: A
Here , P = Rs. 24000 , Rate = 10% per annum = 5% per half year
Time = 1 1 years = 3 half years 2 ∴ C.I. = P 1 + R T − 1 100 C.I. = 24000 1 + 5 3 − 1 100 C.I. = 24000 1 + 1 3 − 1 20 C.I. = 24000 21 3 − 1 20 C.I. = 24000 9261 − 1 8000 C.I. = 24000 9261 - 8000 8000 C.I. = 24000 × 1261 8000 C.I. = 24000 × 1261 = Rs. 3783 8000
- The compound interest on a sum of Rs. 5000 at 8% per annum for 9 months when interest is compound quarterly is :
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When interest is compound quarterly ,
Rate of interest = 8 = 2% per quarter , Time = 3 quarters 4
Here , Principal ( P ) = ₹ 5,000 , Compound Interest ( CI ) = ?
We can find required answer with the help of given formula ,C.I. = P 1 + R T − 1 100 C.I. = 5000 1 + 2 3 − 1 100
Correct Option: C
When interest is compound quarterly ,
Rate of interest = 8 = 2% per quarter , Time = 3 quarters 4
Here , Principal ( P ) = ₹ 5,000 , Compound Interest ( CI ) = ?
We can find required answer with the help of given formula ,C.I. = P 1 + R T − 1 100 C.I. = 5000 1 + 2 3 − 1 100
C.I. = 5000[(1.02)3 - 1]
C.I. = 5000 (1.061208 – 1)
C.I. = 5000 × 0.061208 = Rs. 306.04
- A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs. 840 in 4 years. The rate of interest per annum is :
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Let principal be P.
Given that , A1 = Rs. 800 , T1 = 3 years and A2 = Rs. 840 , T2 = 4 years , R1 = R2 = R%
Using the given formula , we haveA = P 1 + R T 100 ⇒ 800 = P 1 + R 3 ....(i) 100
and,840 = P 1 + R 4 ....(ii) 100
On dividing equation (ii) by (i),840 = 1 + R 800 100 ⇒ 21 = 1 + R 20 100
Correct Option: C
Let principal be P.
Given that , A1 = Rs. 800 , T1 = 3 years and A2 = Rs. 840 , T2 = 4 years , R1 = R2 = R%
Using the given formula , we haveA = P 1 + R T 100 ⇒ 800 = P 1 + R 3 ....(i) 100
and,840 = P 1 + R 4 ....(ii) 100
On dividing equation (ii) by (i),840 = 1 + R 800 100 ⇒ 21 = 1 + R 20 100 ⇒ R = 21 − 1 = 1 100 20 20 ⇒ R = 1 × 100 = 5% per annum 20
