Worked Out Examples

Q1.

Calculate the simple interest if P = Rs. 4800, T = 2 years, R = 8 %?

Sol.

P = 4800Rs, T = 2 years, R = 8 % .....(Given)

Simple interest(SI)	=	PTR/100
	=	(4800 × 2 × 8)/100
	=	48 × 2 × 8
	=	Rs. 768
Hence Simple interest(SI) is Rs. 768

Q2.

Find the simple interest on Rs. 6250 at 4 % per annum for the period from December 27,2002 to May 22, 2003. Also find the amount ?

Sol.

Given

Principal (P) = Rs. 6250, Rate (R) = 4%,

Time (T) = December 27, 2002 to May 22, 2003

The number of days per which the money was kept may be counted as :

Month	December	January	February	March	April	May
Number of days	4	31	28	31	30	22

Time(T)	=	(4 + 31 + 28 + 31 + 30 + 22)days
	=	146 days
Convert the time into years, so divided with 365
Time(T)	=	146/365
	=	(73 × 2)/(73 × 5)
	=	2/5 years
Simple interest(SI)	=	PTR/100
	=	[6250 × (2/5) × 4]/100
	=	(6250 × 2 × 4)/(100 × 5)
	=	100
∴ Simple interest(SI) = Rs. 100 Now, amount = simple interest + principal ∴ Amount = 100 + 6250 = Rs 6350

Q3.

At what rate percent per annum will the amount Rs.72 produce an interest of Rs. 115.20 in 2 years?

Sol.

Given that the principal amount (P) = Rs.72, time(T) = 2 years.

The Simple interest (SI) = Rs.115.20

Now we have to calculate the rate per cent at which the Rs.72 will

produce a simple interest of Rs.115.20

We know that SI = PTR/100

115.20	=	(72 × 2 × R)/100
72 × 2 × R	=	115.20 × 100
R	=	(115.20 × 100)/(72 × 2)
R	=	80%

At 80% of interest the amount Rs.72 will produce a simple interest of Rs.115.20 in 2 years.

Q4.

If Rs.1250 amount to Rs.1550 in 3 years at simple interest, then find the rate of percentage?

Sol.

Given

Principal amount (P) = 1250 Rs, Time(T) = 3 years

Total amount (A) = Rs.1550

Simple interest (SI)	=	total amount – principal amount
	=	A – P
	=	1550 – 1250
	=	Rs. 300
Now we have to calculate the rate of interest (R)
Simple interest	=	PTR/100
300	=	(1250 × 3 × R)/100
1250 × 3 × R	=	300 × 100
R	=	(300 × 100)/(1250 × 3)
R	=	8%

So, the principal Rs. 1250 at the rate 8% per annum will produce Rs. 300 of simple interest in a period of 3 years.

Q5.

Calculate the simple interest and compound interest if principal = Rs. 6000

Rate = 10% and time period = 2 years ?

Sol.

Simple interest	=	PTR/100
	=	(6000 × 2 × 10)/100
	=	600 × 2
	=	Rs. 1200

Now, we have to calculate the compound interest for 2 years

First we will calculate for the first year

Interest on Rs. 6000 for 1 year at the rate of 10% per annum is

Interest for first year	=	PTR/100
300	=	(6000 × 1 × 10)/100
	=	Rs. 100
Amount at the end of first year	=	principal + interest for first year
R	=	6000 + 600
R	=	Rs. 6600

So, Rs. 6600 become the principal amount for the second Year.

Principal for second year (P)	=	Rs. 6600
Rate of interest (R)	=	10%
Time period (T)	=	1 year
So, interest for second year	=	(6600 × 1 × 10)/100
	=	Rs. 660
Amount at the end of second year	=	principal + interest for second year
	=	6600 + 660
	=	Rs. 72602
Compound interest	=	amount at the end of second year – principal
	=	7260 – 6000
	=	Rs. 1260

The interest Rs. 1260 is the compound interest on Rs. 6000 for 2 years at the rate 10%.

Q6.

Find the compound interest on Rs. 8000 at 5% per annum, for 2 years, compounded annually ?

Sol.

Given

Principal amount (P)	=	Rs. 8000
Time (N)	=	2 years
Rate (R)	=	5%
Compound interest	=	P{[1 + (R/100)]^N – 1}
	=	8000{[1 + (5/100)]² – 1}
	=	8000[(21/20)² – 1]
	=	8000[(441/400) – 1]
	=	8000(41/400)
	=	Rs. 820
Hence, compound interest is Rs. 820

Q7.

What is the amount to be paid on a loan of Rs. 62500 for 3/2 years at 8 % per annum, compounded half – yearly?

Sol.

Given

Principal amount (P)	=	Rs. 62500
Rate (R)	=	8%
Time (N)	=	3/2 years
Here the interest is calculated half-yearly So R = R/2 = 8/2 = 4% and 2N = 2 × (3/2) = 3 years
Compound interest	=	P{1 + [(R/2)/100]}^2N
	=	62500{[1 + (4/100)]³ – 1}
	=	62500{(26/25)³ – 1}
	=	62500{[(26)³ – (25)³]/[25]³}
	=	62500{(17576 – 15625)/15625}
	=	62500(1951/15625)
	=	[15625 × 4]×(1951/ 15625)
	=	4 × 1951
	=	Rs. 7804
Hence, compound interest is Rs. 7804