# Simple Interest-practice test

1.

My cousin lends me Rs.10 lakhs for studying in United States at 8% compound interest per annum, during the course period of 2 years and at 12% per annum after completion of my studies. If I return 50% of the amount which is to be returned on completion of studies, and the remaining after one year, how much interest must I pay him during the whole period in Lakhs?

A   1.12
B   2.36
C   2.72
D   3.06

Explanation:

Amount which is to be returned on completion of studies = 10,00,000 [(1+8/100)^2]

=Rs.11,66,400

But amount which is returned on completion of studies =11,66,400/2 = Rs.5,83,200

Amount which is returned after one year of completion of studies =5,83,200 [(1+12/100)^1] = Rs.6,53,184

: . Total amount returned = 5,83,200 + 6,53,184 = Rs.12,36,384

: . Interest paid = 12,36,384 – 10,00,000 = Rs.2,36,384 = Rs.2.36 lakhs

2.

The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?

A   6000
B   6400
C   7200
D   9600

3.

Pradeep invested some money in 10% stock at Rs.96. If Pramod wants to invest in an equally good 12% stock, he must purchase a stock worth of:

A   Rs 80.00
B   Rs.115.20
C   Rs.120.00
D   Rs.125.40

Explanation:

For an income of Rs.10, investment = Rs.96

For an income of Rs.12, investment = Rs.(96/10)* 12 = Rs. 115.20

4.

The total capital investment in setting up a production unit is Rs.15 lakhs and the production unit produces 3 million kg of product annually. Selling price of product is 9 per kg. Manufacturing cost include raw material at the rate Rs.0.8 per kg, labour at the rate 1.2 per kg, packing at the rate of 0.6 per kg and utilities at the rate of 0.8 per kg. General expenses comes out to be 15% of manufacturing cost. If taxes are considered as 33% of gross annual earnings, determine the net profit of the production unit per year?
A   0.5 crores
B   1.02 crores
C    1.5 crores
D    2 crores

Explanation:

Manufacturing cost = 3.4 per kg. (0.8 +1.2+.6+.8)

General expenses = 0.15 * 3.4 = 0.51 per kg

Total cost = 3.4 +0.51 = 3.91

Profit = 9-3.91 = 5.09

Profit for 3 million kg of product = 5.09 *30,00,000 = Rs. 1,52,70,000 = Rs.1.52 crores

Tax = .33 *1.52 = 0.5016 crores.

Net profit = 1.52 –0.50 = 1.02 crores.

5.

A man deposited Rs.40,000 in a bank at 10% per annum interest compounded yearly. Now after two years, the government comes out with a law that any annual interest greater than Rs.2500 will be taxed at the end of the year. Also, the rate of interest is decreased to 8%. How much should the man withdraw now so as, not to pay tax at the end of the year?

A   Rs.16750
B   Rs.23000
C   Rs.17150
D   Rs.8750

Explanation:

Amount (including C I at end of two years) = 4000 *1.1*1.1 = Rs.48400

For annual interest of Rs.2500 at 8%, principle amount that should be deposited = 2500/0.08 = Rs.31250.

Amount that should be withdrawn = 48400 – 31250 = Rs.17150.

6.

The compound interest on a certain sum for 2 years is Rs.1100 and the simple interest is Rs.1000. If this sum is invested such that the simple interest is Rs.400 and the number of years is equal to rate percent per annum, find the new rate percent.

A   2%
B   4%
C   8%
D   16%

Explanation:

Simple interest for one year= 1000/2= Rs.500
Compound interest for 1 year= Simple interest for 2 years+ Simple interest on Simple interest of 1 year= 500 * 2 +100
:. Rate of interest= 100*(100/500)= 20%
Hence, sum= 500 * (100/20)= 2,500
Now this money is again invested
Let n be number of years and rate of interest
:. 400= (2500 * n2)/100 :.n= 4

7.

A man invested 3/3 of his capital at 7% , 1/4 at 8% and the remainder at 10% If his annual income is Rs.561. The capital is:

A   5200
B   6600
C   4800
D   none of these

Explanation:

Let the capital be Rs. x.

Then, (x/3 + 7/100 + 1) + (x/4 + 8/100 + 1) + (5x/12 + 10/100 +1) = 561

7x/300 + x/50 + x/24 = 561

51x = 561 * 600

x = 6600.

8.

A bank pays interest @ 8 percent p.a. on a deposit for half a quarter as well as on a deposit for one quarter. A makes a deposit of Rs.25 lakhs for a quarter. B makes a deposit of Rs.25 lakhs for half a quarter, and after maturity reinvests the entire amount for half a quarter. What is B’s gain over A?

A   Rs.200
B   Rs.225
C   Rs.250
D   Rs.275

Explanation:

A’s interest =25 lakhs*2/100 = 50,000
B’s interest = 25 lakhs * (101/100) * (101/100) – 25 lakhs = 50,250
:. B’s gain over A = 250.

9.

A certain sum becomes 8 times itself in 3 years under compound interest, interest being compounded annually. How many years would the sum takes to become 64 times itself?

A   12
B   8
C  6
D   3

Explanation:

A= P(1+ r/100)n

8P=P(1+ r/100)3

Let 1+ r/100 be R

8=R3

R=2

Let the sum become 64 times itself in n years.

64P=PRn

64=2n; n=6 years.

10.

What is the simple interest on Rs.6500 at 13% p.a. for 4 years?
A   Rs.3280
B    Rs.3350
C    Rs.3250
D    Rs.3380

Explanation:

S.I. = (6500*4*13)/100 = Rs.3380