QUESTIONS ON SIMPLE & COMPOUND INTEREST (MIXED)

QUERY 1

At a certain rate p.a. the SI on a sum of money for one year is Rs. 260 and the CI on the same sum for two years is Rs. 540.80. The rate of interest per annum is

A) 4
B) 6
C) 8
D) 10

MAHA GUPTA
SI on 260 for 1 year = 540.80 – (2*260) = 20.80
To find the rate of interest we have to see only what percentage of 260 is 20.80
Obviously it will be (20.80*100)/260 = 8 (option ‘C’)

QUERY 2

If the difference between the compound interest and simple interest on a sum at 5% rate of interest per annum for 3 years is Rs 36.60; then the sum is?

A) 8000
B) 8400
C) 4400
D) 4800

MAHA GUPTA
Formula for difference between CI and SI for 3 years = Pr²(3 +r); where P is the initial sum and ‘r’ means r/100

Therefore 36.60 = P[(5/100)²)(3 + 5/100)
=> 3660/100 = (61/8000)P
=> P = 4800 (option ‘D’)

SHORT
Instead of using of the above formula do it by answer options. You’ll see option ‘A’ and ‘B’ are ruled out straightaway. Now check with options ‘C’ or ‘D’.

QUERY 3

The difference between the compound interest and simple interest on a certain sum for 2 yrs at 10% per annum is Rs. 300. Find the sum.

A) 31500
B) 30000
C) 30500
D) 31000

MAHA GUPTA
Formula for difference between CI and SI for 2 years = Pr², where P is the initial sum and ‘r’ means r/100

Therefore 300 = P[(10/100)²)
=> 300*100 = P
=> P = 30,000 (option ‘B’)

SHORT
Instead of using of the above formula do it by answer options.

QUERY 4

On what sum of money will compound interest of two years be the same at same rate of interest as the simple interest on Rs 416 for 10 years at 8% per annum?

A) 2000
B) 1500
C) 3000
D) 3500

MAHA GUPTA
Simple Interest on 416 for 10 years at 8% = 416*10*8/100 = 1664/5

If compound interest is to be calculated for 2 years at 8% per annum it will be equal to 8 + 8 + (8*8)/100 = 16.64% for 1 year.

So, if 16.64 is the CI, the initial sum = 100
If 1664/5 is the interest, the sum = (100/16.64)*(1664/5) = 2000 (option ‘A’)

QUERY 5

At a certain rate per annum, the simple interest on a sum of money for one year is Rs 260 and the compound interest on the same sum for 2 years is 540.80. Find the rate of interest.

A) 5%
B) 10%
C) 8%
D) 16%

MAHA GUPTA
As the CI is given for 2 years, also calculate the SI for 2 years so that difference of interests for 2 years could be known

SI for 2 years = 260*2 = 520
So, the difference in CI and SI for 2 years = 540.80 – 520 = 20.80

As the (CI – SI) is the result of interest on interest, so obviously 20.80 is interest on 260 for 1 year because CI and SI are always equal in the first year

Now interest on 260 for 1 year = 20.80
Therefore interest on 100 for 1 year = 8 (option ‘C’)

QUERY 6

The difference between the simple interest on a certain sum at the rate of 10% per annum for 2 years and compound interest which is compounded every 6 months is Rs 124.05. What is the principal?

A) Rs 4500
B) Rs 5800
C) Rs 8000
D) Rs 12000

MAHA GUPTA
The CI is compounded half yearly for two years means 4 terms

SI rate annually is 10%, means 5% half yearly

The formula for difference between CI and SI for 4 terms = Pr²[6 + 4r + r²]; where P = principal, and ‘r’ means r/100

Therefore P[(5/100)²]*[6 + 4(5/100) + (5/100)²] = 124.05
=> P*(1/400)*(2481/400) = 12405/100
=> P = (12405/100)*(1,60,000/2481)
=> P = 8000 (option ‘C’)

QUERY 7

A certain sum amounts to Rs. 7350 in 2 years and to Rs 8575 in 3 years. Find the sum and rate percentage?

A) 20%
B) 18%
C) 25%
D) 50/3%

MAHA GUPTA
When the manner of rate of interest is not given, it’s treated to be simple rate of interest. So if in the exam such is a question always take it as simple interest; not the compound interest.

Interest for 3rd year = amount of three years – amount of two years = 8575 – 7350 = 1225

Therefore interest for 2 years = 1225*2 = 2450
Hence the sum in the beginning = 7350 – 2450 = 4900

Now the principal = 4900; interest = 2450; time = 2 years

So rate = (interest *100)/(principal*time) = (2450*100)/(4900*2) = 25%

So sum = 4900; Rate = 25% (option ‘C’)

QUERY 7

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re 1. The sum (in rupees) is?

A) 625
B) 630
C) 640
D) 650

MAHA GUPTA
Formula for difference between CI and SI for 2 years = Pr², where P is the initial sum and ‘r’ means r/100

Therefore 1 = P[(4/100)²)
=> 1*625 = P
=> P = 625 (option ‘A’)

SHORT
Instead of using of the above formula do it by answer options.

QUERY 8

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?

A) Rs 2160
B) Rs 3120
C) Rs 3972
D) Rs 6240

MAHA GUPTA
There is 60% increase in the amount in 6 years at simple interest, means rate of interest = 60/6 = 10% per annum.

Therefore, CI = 12000*(1 + ¹⁰⁄₁₀₀)³ – 1
= Rs 12000*(331/1000)
= Rs 3972 (option ‘C’)

QUERY 9

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is?

A) Rs 1550
B) Rs 1650
C) Rs 1750
D) Rs 2000

MAHA GUPTA
Obviously we need to calculate the compound interest first
So, CI = 4000(1 + ¹⁰⁄₁₀₀)² – 4000
= Rs 840

But the simple interest is half of the compound interest
Hence, SI = ⁸⁴⁰⁄₂ = Rs 420

Therefore the sum placed on SI = ^(420*100)⁄_(3*8) = Rs 1750 (option ‘C’)