Question

9. Rajesh borrowed 50000 from Vijay at simple interest of 12% per annum for 2 years, but lent it
to Sunder on the same day at 12% per annum compound interest for 2 years. Find his gain after
2 years.​

Answer 1

Given : Rajesh borrowed 50000 from Vijay at simple interest of 12% per annum for 2 years,  

lent it to Sunder on the same day at 12% per annum compound interest for 2 years.

To Find  : his gain after 2 years.​

Solution:

P = 50000

R = 12 %

T = 2 Years

SI = P * R * T /100

= 50000 * 12 * 2 /100

= 12000

CI  = 50000(1 + 12/100)² - 50000

=> CI  = 50000(1.12)² - 50000

=>  CI  = 50000{(1.12)² - 1}

=> CI = 12,720

Gain = 12720 - 12000 = rs 720

Another Simpler method :

Interest earned in 1st year = 50000 * 12 * 1 /100 = 6000

Gain is the interest earned in 2nd year on interest earned in 1st year

Gain = 6000 * 12 * 1 /100  = 720 Rs

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Answer 2

Answer:

₹ 90

EXPLAINATION

Given:

Present value =₹16000

Interest rate =7

2

1

​

%perannum= 15/2 \%$$

Time =2 years

To find the amount we have the formula,

Amount (A)=P(1+(r/100))

n

where P is the present value, r is the rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴A=16000(1+(15/2)/100)

2

⇒A=16000(1+3/40)

2

⇒A=16000(43/40)

2

⇒A=16000(1894/1600)

⇒A=₹ 18490

Now, we find the compound interest,

∴ Compound interest =A–P

=18490–16000=₹ 2490

Now we find the simple interest,

Simple interest (SI)=PTR/100

where P is principle amount, T is time taken, R is rate per annum

SI=(16000×(15/2)×2)/100

=160×15

=₹ 2400

Abhay's gain at the end of 2 years=(CI–SI)

=2490–2400

=₹ 90