Compound Interest- Aptitude Questions and Answers

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The difference between the simple and the compound interest compounded every six months at the rate of 10 percent per annum at the end of two years is Rs 124.05. What is the sum ?

A)
Rs. 10000

B)
Rs. 6000

C)
Rs. 12000

D)
Rs. 8000


Correct Answer :

Rs. 8000


Explanation :

Let Principal = P, Rate = R% per annum, Time = n years.
Compound Interest, CI = P* [ 1 + (R/2)/100 ]2n - P , if compound interest is half-yearly
Simple Interest, SI = P*R*T / 100

Then,CI - SI = ( P*(1 + 5/100)4 - P ) - ( P* 10* 2 / 100 ) = 124.05
P*(21/20)4 - P - P/ 5 = 124.05
P*(194481 - 160000 - 32000 ) / 160000 = 124.05
P = 19848000 / 2481
P = 8000

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The difference between compound and simple interests on a certain sum for 2 years at 5% per annum is Rs.40. The sum is?

A)
Rs.16,000

B)
Rs.15,000

C)
Rs.12,000

D)
Rs.10,000


Correct Answer :

Rs.16,000


Explanation :

Let the sum be rs X then,
CI = X*( 1 + 5/100 )2 - X = X*(441 / 400 - 1) = X*41 / 400
SI = X*5*2 / 100 = X / 10

As is given, CI - SI = 40
X* ( 41 / 400 - 1 / 10) = 40
X* (41 - 40) / 400 = 40
X = 16000

If Rs 7500 are borrowed at compound interest at the rate of 4% per annum, then after 2 years the amount to be paid is ?

A)
Rs. 8082

B)
Rs. 7800

C)
Rs. 8100

D)
Rs. 8112


Correct Answer :

Rs. 8112


Explanation :

Amount = P*(1+ R/100 )n , if interest is payable annually
Amount = 7500*(1 + 4/100 )2
= 7500 * (104/100)2
= 7500 * (26/25)2
= 7500 * 26/25 * 26/25
= 8112

The compound interest on Rs 2800 for 11/2 years at 10% per annum is ?

A)
Rs. 441.35

B)
Rs. 436.75

C)
Rs. 434

D)
Rs. 420


Correct Answer :

Rs. 434


Explanation :

Let Principal = P, Rate = R% per annum, Time = n years.
When time is fraction of a year, say 43/4 years, then amount= P(1+R/100)4 x (1+(3R/4)/100)

So, Amount = 2800 * (1 + 10/100) * (1 + (1*10/2) / 100)
= 2800 * (1 + 10/100) * (1 +5/100)
= 2800 * 11/10 * 21/20
= 3234

Required C.I. = (3234 - 2800) = 434

A money lender lends Rs 2000 for 6 months at 20% per annum whereas the interest is compounded quarterly. After the given period he will get the amount of ?

A)
Rs. 2205

B)
Rs. 2200

C)
Rs. 2160

D)
Rs. 2040


Correct Answer :

Rs. 2205


Explanation :

Let Principal = P, Rate = R% per annum, Time = n years.
Amount = P(1 + (R/4)/100 )4n , if interest is payable quarterly

Hence,required amount = 2000* (1 + (20/4) / 100 )4*1/2
= 2000*(1 + 5/100)2
= 2000*(21 / 20)2
= 2205

The compound interest on a certain sum of money for 2 years at 10% per annum is Rs 420. The simple interest on the same sum at the same rate and for the same time will be ?

A)
Rs. 350

B)
Rs. 375

C)
Rs. 380

D)
Rs. 400


Correct Answer :

Rs. 400


Explanation :

Let the principle is P.
As is given, compound interest= P*(1 +10/100)2 - P = 420
P*(11/10)2 - P = 420
P*(121/100) - P = 420
P*(121-100)/100 = 420
P = 2000

So, simple interest.= P*R*T / 100 = 2000* 2* 10 / 100 = 400

In what time will Rs 90600 amounts to Rs 109626 at 10% compound Interest?

A)
2 years

B)
3 years

C)
5 years

D)
4 years


Correct Answer :

2 years


Explanation :

Amount = P(1+R/100)n , if compound interest is payable annually
Then, 109626 = 90600*(1 + 10/100)n
109626 / 90600 = (11/10)n
(121/100) = (11/10)n
(11/10)2 = (11/10)n
n = 2 years

Compound interest on a certain sum of money at 20% per annum for 2 years is Rs 5995. What is the simple interest on the same money at 8% per annum for 6 years ?

A)
Rs. 5989

B)
Rs. 6789

C)
Rs. 6540

D)
Rs. 7844


Correct Answer :

Rs. 6540


Explanation :

Let Principal = P, Rate = R% per annum, Time = n years.
Compound Interest, CI=P(1+R/100)n - P
Then, 5995 = P*(1 + 20/100)2 - P
5995 =P*(36/25 - 1)
5995 = P* 11/25
P = 5995*25 / 11
P = 13625

Hence Simple Interest, SI = P*R*T / 100 = 13625 * 8 * 6 / 100 = 6540

On a simple interest rate of 20% annually, a trader gets 6000 rupees in 3 years. How much he gets more if the lent was on compound interest ?

A)
1200

B)
480

C)
4000

D)
400


Correct Answer :

480


Explanation :

Let Principal = P, Rate = R% per annum, Time = n years.
Simple Interest , SI = P*R*T /100
Amount = P + Simple Interest =P + (P*R*T/100) = 6000
P + P*20*3 /100 = 6000
P = 6000*5/8 = 3750
Thus, Simple Interest in 3 years, SI = 6000 - 3750 = 2250

Compound Interest, CI=P*(1 + R/100)n - P
CI = 3750*(1 + 20/100)3 - 3750
=3750*[ (6/5)3 -1 ]
=3750*( 91/125 ) =2730

Hence, trader will be get more if the lent was on CI = CI - SI = 2730 - 2250 = 480

The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is Rs 1.50 . The sum is ?

A)
600

B)
500

C)
400

D)
300


Correct Answer :

600


Explanation :

Let the sum is 100 then
S.I. = 100* 5* 2 / 100 = 10
C.I = 100 *(1 + 5/100)2 - 100 = 41/4
Difference between C.I and S.I = 41/4 - 10 = 0.25

So, 0.25 : 1.50 : : 100 : P
∴ P = (1.50 * 100) / 0.25 = 600

If the compound interest on a certain sum for 2 years at 12.5% per annum is 170, the simple interest will be?

A)
200

B)
150

C)
160

D)
170


Correct Answer :

160


Explanation :

Let the principle is P
So compound interest = P * ( 1 + 12.5/100)2 - P = 170
P* (112.5/100) *(112.5/100) - P = 170
P* (12656.25 - 10000) / 10000 = 170
∴ P = 1700000 / 2656.25

Simple interest SI = P* T* R /100
= (1700000 / 2656.25)* 2* 12.5 / 100
= 160

Albert invested an amount of Rs 8000 in a fixed deposit scheme for 2 years at compound interest rate 5% annum . How much amount will Albert get on maturity of the fixed deposit ?

A)
Rs. 8600

B)
Rs. 8620

C)
Rs. 8820

D)
Rs. 8840


Correct Answer :

Rs. 8820


Explanation :

Amount= 8000*(1 + 5/100)²
= 8000* 21/20* 21/20
= 8820

A man borrows 12500 from a bank at 20% compound interest. At the end of every year he pays 2000 as part repayment. How much (in rupees) does he still owe to the bank after three such instalments?

A)
15600

B)
12864

C)
13780

D)
14320


Correct Answer :

14320


Explanation :

Remaining amount after 1 year = 12500 *(120/100) - 2000 = 13000
Remaining amount after 2 year = 13000*(120/100) - 2000 = 13600
Remaining amount after 3 year = 13600*(120/100) - 2000 = 14320

A sum of 2400 deposited on compound interest, doubled after 5 years. How much will it be after 20 years?

A)
24000

B)
38400

C)
19200

D)
14320


Correct Answer :

38400


Explanation :

2P = P *(1 + R/100)5
24 P = P *(1 + R/100)20

The amount becomes 24 times = 16 times and required amount = 2400*16 =38400

In how many years Rs 800 will be Rs 882 at 5% per annum if compounded annually?

A)
1 year

B)
2 years

C)
3 years

D)
4 years


Correct Answer :

2 years


Explanation :

amount = P ( 1 + R/100 )n
As is given, 882 = 800*( 1 + 5/100 )n
882/800 = (21/20)n
441/400 = (21/20)n
(21/20)2 = (21/20)n
N=2

How much will the compound interest at the rate of 15/2% annually in 2 years on 6400 rupees?

A)
1016

B)
996

C)
976

D)
966


Correct Answer :

996


Explanation :

compound interest, CI= 6400* (1 + (15 / 2) / 100 )2 - 6400
= 6400* (1 + 15 / 200 )2 - 6400
= 6400* (43 / 40 )2 - 6400
= 6400* (1849 / 1600) - 6400
= 6400* (1849 / 1600 - 1)
= 6400* 249 / 1600 = 996

The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 2 years is 10 rs. What is the sum ?

A)

5,000


B)

6,000


C)

6,250


D)

7,500



Correct Answer :

6,250


Explanation :

Let the sum is 100 then
S.I. = 100* 4* 2 / 100 = 8
C.I = 100 *(1 + 4/100)2 - 100 = 100*( 26/25) 2 - 100 = 204/25
Difference between C.I and S.I = 204/25 - 8 = 4/25 = .16

So, 0.16 : 10 : : 100 : P
∴ P = (10* 100) / 0.16 = 6250

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