simple and compound Intrest questions and solutions

Question : A sum of money amounts to Rs.53200 at 11% simple interest in 3 years. Find the sum.
Option 1 : Rs.40000
Option 2 : Rs.38900
Option 3 : Rs.33100
Option 4 : Rs.17024
Explanation : Let the sum be Rs.x
SI = x*11*3/100
= 33x/100

P+SI = A
x+(33x/100) = 53200
133x = 5320000
x=40000

Question : A sum of Rs.20000 is compounded annually at an interest rate of 10%. How much does it amount to after 2 years?
Option 1 : Rs.24420
Option 2 : Rs.24400
Option 3 : Rs.24000
Option 4 : Rs.24200
Explanation : A = P[1+(R/100)]^n
= 20000[1+(10/100)]²
= 20000[1.1]²
= 20000*1.21
= Rs.24200

Question : I borrowed two equal amounts, one at 12% S.I. for 2 years and the other at 10% for 3 years respectively. If the difference in the interest was Rs.1200 , find the total amount borrowed.
Option 1 : Rs.20000
Option 2 : Rs.30000
Option 3 : Rs.40000
Option 4 : Rs.50000
Explanation : Let the amount borrowed be Rs.x

SI on the first amount
= 12*2*x/100
= 24x/100
SI on the second amount
= 10*3*x/100
= 30x/100
Difference in the interests
= 6x/100 = 1200
Solving,
x=Rs.20000
Total amount
=Rs.40000

Question : A sum of Rs.50000 was divided into two parts and the first part was deposited at 10% simple interest and the second part at 8% interest. At the end of two years, the interest earned was Rs.8800 . Find the amount deposited at 8% interest.
Option 1 : Rs.20000
Option 2 : Rs.30000
Option 3 : Rs.25000
Option 4 : Rs.24000
Explanation : Let the sum be divided into Rs.x and Rs.y
x+y=50000
x=50000-y
Interest on the first part
= x*2*10/100
= 20x/100
Interest on the second part
= y*2*8/100
= 16y/100
Total interest
[(20(50000-y))+16y]/100 = 8800
1000000-20y+16y=880000
4y=120000
y=30000

Question : Find the simple interest on a sum of Rs.80000 at 8% interest for 8 years.
Option 1 : Rs.51200
Option 2 : Rs.64000
Option 3 : Rs.6400
Option 4 : Rs.8000
Explanation : SI=PTR/100
=80000*8*8/100
=51200

Question : If the compound interest on a certain sum at 5% for 2 years is Rs.512.50, what would be the  simple interest?
Option 1 : Rs.500
Option 2 : Rs.510
Option 3 : Rs.450
Option 4 : Rs.512.5
Explanation : A = P[1+(R/100)]²

P+512.5 = P*(105/100)²

P+512.5 = 1.1025P

0.1025P = 512.5

P=5000

SI = 5000*2*5/100 = Rs.500

Question : The compound interest on a certain sum at a certain rate of interest for the 1st year is Rs.1200 and for the 2nd year is Rs.1344. Find the rate of interest.
Option 1 : 12.5%
Option 2 : 8%
Option 3 : 12%
Option 4 : 10%
Explanation : At the end of 1 year,
A = P[1+(R/100)]
P+1200 = P+(PR/100)
PR = 120000

At the end of 2 years,
A = P[1+(R/100)]²
P+1200+1344 = P+(2PR/100)+(PR²/10000)

Substitute PR=120000,
2544 = (2*120000/100)+(120000R/10000)
Solving,
R=12%

Question : Rs.20000 is invested at 11% compound interest for 2 years. Find the interest in the second year.
Option 1 : Rs.4642
Option 2 : Rs.2200
Option 3 : Rs.4400
Option 4 : Rs.2442
Explanation : After 1 year,
A = 20000[1+(11/100)]
= Rs.22200
I = Rs.2200
After 2 years,
A = 20000[1+(11/100)]^2
= Rs.24642
I = Rs.4642
Interest in the second year
= 4642-2200
= Rs.2442

Question : A borrows an amount of Rs.15000 from B at 8% simple interest and lends it to C at 10% interest. How much does B gain after 2 years?
Option 1 : Rs.1500
Option 2 : Rs.600
Option 3 : Rs.200
Option 4 : Rs.400
Explanation : Interest paid by B to A
= 15000*2*8/100
= 2400
Interest paid by C to B
= 15000*2*10/100
= 3000
B gains Rs.600.

Alternatively, B gains (10-8)=2% of 15000.

Question : On simple interest, a sum of Rs.5000 amounts to Rs.6200 in 3 years at a given rate of interest. How much would it amount to if the interest rate is increased by 2%?
Option 1 : Rs.6725
Option 2 : Rs.6800
Option 3 : Rs.7500
Option 4 : Rs.6500
Explanation : Interest=Rs.1200

I=PTR/100

1200=5000*3*R/100

R=8%

R1=10%
I1=5000*3*10/100
= 1500

A1=Rs.6500

Question : Amar and Amit divide Rs.100000 between them and deposit it in a bank at 8% simple interest. At the end of 5 years, Amar's share is R.28000 more than that of Amit. Find the ratio in which they divided the original amount.
Option 1 : 3:2
Option 2 : 5:4
Option 3 : 4:3
Option 4 : 5:3
Explanation : Let Amar's original share be P1 and Amit's share be P2.
P1+P2=100000

SI1 = P1*5*8/100
= 0.4P1
A1 = P1+SI1
= 1.4P1

SI2 = 0.4P2
A2 = 1.4P2

A1 - A2 = 28000
1.4P1-1.4P2=28000

P1-P2=20000
P1+P2=100000

Solving,
P1=60000
P2=40000
P1:P2=3:2

Question : How long does it take for a sum of Rs.2500 to become Rs.12500 at 10% simple interest?
Option 1 : 40 years
Option 2 : 50 years
Option 3 : 25 years
Option 4 : 49 years
Explanation : SI = PTR/100
= 2500*T*10/100
= 250T

P+SI = A

2500+250T = 12500

10+T = 50

T = 40 years

Question : The rate of growth of population of a village has been compounding annually at a constant rate of 5%. If the present population of the village is 10000, find the population after two years.
Option 1 : 10500
Option 2 : 11025
Option 3 : 15000
Option 4 : 10250
Explanation : The current population is taken as P.

Population after 2 years
= 10000[((1+(5/100))²]
= 11025

Question : The difference between the compound and simple interest on Rs.40000 for 2 years at the same rate of interest is Rs.400. Find the rate of interest.
Option 1 : 12%
Option 2 : 4%
Option 3 : 8%
Option 4 : 10%
Explanation : SI = 40000*2*R/100
= 800R

CI = [40000(1+(R/100))²]-40000
= 40000[(1+(R/100))²-1]
= 40000[1+(2R/100)+(R²/10000)-1]
= 800R+4R²

CI-SI = 400

4R²+800R-800R = 400

R²=100

R=10%

Question : A sum of Rs.7500 at compound interest at 4% per annum for 2 years amounts to
Option 1 : Rs.7800
Option 2 : Rs.8100
Option 3 : Rs.8112
Option 4 : Rs.8082
Explanation : A = P[1+(R/100)]^n
= 7500[[1+4/100]²
= 7500[1.04]²
= Rs.8112

Question : An amount increases by 40% in 5 years at simple interest. By how much % does it increase in 2 years at the same rate on compound interest?
Option 1 : 21%
Option 2 : 17.28%
Option 3 : 16.64%
Option 4 : 13.31%
Explanation : S.I = 0.4P = P*5*R/100
R=8%
A = P[1+(8/100)]^2 = P[1.08]^2 = 1.1664P
It increases by 16.64%

Question : At what rate of compound interest will a sum of Rs.8000 amount to Rs.8820 in two years?
Option 1 : 8%
Option 2 : 10%
Option 3 : 6%
Option 4 : 5%
Explanation : 8820 = 8000[(1+(R/100))²]

[1+(R/100)]² = 8820/8000 = 1.1025 = (1.05)²

R = 5%

Question : Simple interest on Rs.3500 for 2 years at 9% interest is equal to the compound interest on a certain sum of money for the same number of years at 10% per annum. Find the sum of money.
Option 1 : Rs.3310
Option 2 : Rs.3000
Option 3 : Rs.3500
Option 4 : Rs.6300
Explanation : S.I = 3500*2*9/100 = Rs.630

C.I = P[(1+(10/100))^2] – P
= P[(1.1)^2 – 1]
= 0.21P
= 630
P = Rs.3000

Question : If the simple interest on a certain sum of money for 3 years at 10% interest is Rs.300, find the compound interest on the same sum for the same time at the same rate of interest.
Option 1 : Rs.300
Option 2 : Rs.321
Option 3 : Rs.210
Option 4 : Rs.331
Explanation : P = 300*100/(3*10) = Rs.1000

A = 1000*(1+(10/100))^3 = 1331

C.I = 1331-1000 =Rs.331

Question : The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is
Option 1 : 3
Option 2 : 4
Option 3 : 5
Option 4 : 6
Explanation : A>2P
P((1+(20/100))^n) >2P
(1.2)^n>2
By trial and error,
1.2^2=1.44
1.2^3=1.728
1.2^4=2.0736
Least possible value of n=4

Question : Ram and Shyam deposit an equal amount of money in a bank at simple interest. Ram deposits for a time thrice as long as Shyam at two-thirds of Shyam’s interest rate. Find the ratio of the interests received by Ram and Shyam.
Option 1 : 2:3
Option 2 : 2:1
Option 3 : 3:2
Option 4 : 1:2
Explanation : Let the amount be Rs.P

= P*T*R/100
=[ P*3T*(2/3)R]/100
= 2PTR/100
Ram’s Interest:Shyam’s Interest = 2:1

Question : A finance company claims to lend money at simple interest, but includes the interest every six months for calculating the principal. If they charge an interest of 8%, what is the effective rate of interest?
Option 1 : 8.5%
Option 2 : 8%
Option 3 : 8.16%
Option 4 : 9%
Explanation : Consider a sum of Rs.100

Interest for the first 6 months
= 100 * ½ *8/100
= Rs.4
Interest for the next 6 months
= 104 * ½ *8/100
= Rs.4.16
Interest at the end of 1 year
= Rs.8.16 for a sum of Rs.100

Effective rate of interest = 8.16%

Question : The difference between compound interest and simple interest on a sum of Rs.10000 for 2 years at a rate of 5% interest is
Option 1 : Rs.25
Option 2 : Rs.20
Option 3 : Rs.10
Option 4 : Rs.5
Explanation : S.I = 10000*2*5/100 = 1000

C.I = [10000(1+(5/100))^2)] - 10000 = 1025

C.I-S.I = Rs.25

Question : A lends a sum of Rs.15000 to B at an interest rate of 8%. B uses Rs.5000 and he lends the remaining amount to C. At what rate should B lend the amount to C so that the interest received by B will equal the interest payable by B to A?
Option 1 : 8%
Option 2 : 10%
Option 3 : 12%
Option 4 : 24%
Explanation : 15000*T*8/100 = 10000*T*R/100
R = 15*8/10 = 12%

Question : A sum of money amounts to Rs.49440 in three years and Rs.50400 in five years at the same interest rate. Find the rate of interest per annum.
Option 1 : 10%
Option 2 : 9%
Option 3 : 9.6%
Option 4 : 8%
Explanation : Interest for 2 years
= 50400-49440
= Rs.960
Interest for 3 years
= 3*960/2
= Rs.1440
Principal = 49440-1440 = Rs.48000
1440 = 48000*3*R/100
R=10%

Question : Ganesh lends an amount of Rs.15000 to Arun for 3 years and an amount of Rs.25000 to Varun for 2 years at the same interest rate. The total interest received by him is Rs.9500. Find the rate of interest.
Option 1 : 7%
Option 2 : 8%
Option 3 : 9%
Option 4 : 10%
Explanation : (15000*3*R/100)+(25000*2*R)/100 = 9500

Solving this, R=10

Question : How many years does it take for an amount of Rs.20000 to fetch an interest of Rs.8400 at 7% interest?
Option 1 : 5 years
Option 2 : 5.5 years
Option 3 : 6 years
Option 4 : 7 years
Explanation : I = PTR/100
8400 = 20000*T*7/100
T=6

Question : A sum of money fetched an interest of Rs.3840 in 4 years at an interest rate of 8%. Find the sum.
Option 1 : Rs.8000
Option 2 : Rs.12000
Option 3 : Rs.16000
Option 4 : Rs.19200
Explanation : I = PTR/100
3840 = P*4*8/100
P = Rs.12000

Question : On Simple Interest, a given sum amounts to an interest equal to 9/25 of the sum. Find the rate of interest if it is numerically equal to time.
Option 1 : 3%
Option 2 : 4%
Option 3 : 5%
Option 4 : 6%
Explanation : I = P*T*R/100
(9/25)P = P*R*R/100
R = 6%

Question : Ram lends a sum of money to Shyam at an interest rate of 5% p.a. After two years, he charges an interest of 8% p.a. At the end of five years, Shyam pays Rs. 13400 to Ram, how much money did he initially borrow?
Option 1 : Rs.8000
Option 2 : Rs.9000
Option 3 : Rs.10000
Option 4 : Rs.10500
Explanation : Let the sum of money be Rs.x
Total Interest
= (x*2*5/100) + (x*3*8/100)
= 0.34x
x+0.34x = 1.34x = 13400
x = Rs.10000

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