Question

Mahesh borrowed ₹16000 at 7½% per annum simple interest. On the same day he lent it to Gagan at the same rate but compounded annually. What does he gain at the end of 2 years?

Answer 1

AnswEr :

$\bold{Given} \begin{cases}\sf{Principal=Rs. 16000} \\ \sf{Rate=7 \dfrac{1}{2} \%= \dfrac{15}{2} \: p.a.}\\ \sf{Time=2\: Yr. }\end{cases}$

• According to the Question Now :

$\implies\tt{Gain = Compound \: Interest - Simple \:Interest}$

$\implies\tt{Gain = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{t} - 1 \bigg]- \bigg[\dfrac{PRT}{100} }\bigg]$

$\implies\tt{Gain = \bigg[16000 \bigg(1 + \cancel\dfrac{15}{200}\bigg)^{2} - 1 \bigg]- \bigg[\dfrac{\cancel{16000} \times 15 \times 2}{ \cancel{200}} }\bigg]$

$\implies\tt{Gain = \bigg[16000 \bigg(1 +\dfrac{3}{40}\bigg)^{2} - 1 \bigg]- \bigg[80 \times 15 \times 2}\bigg]$

$\implies\tt{Gain = \bigg[16000 \bigg(\dfrac{43}{40}\bigg)^{2} - 1 \bigg]- \bigg[80\times 30}\bigg]$

$\implies\tt{Gain= \bigg[16000 \bigg(\dfrac{1849}{1600} -1 \bigg) \bigg]- \bigg[2400}\bigg]$

$\implies\tt{Gain= \bigg[\cancel{16000} \times \dfrac{1849 -1600}{ \cancel{1600}}\bigg]- \bigg[2400}\bigg]$

$\implies\tt{Gain = \bigg[10 \times 249\bigg]-\bigg[2400}\bigg]$

$\implies\tt{Gain=Rs.(2490 - 2400)}$

$\implies\large\boxed{ \tt Gain =Rs. 90}$

⠀

∴ Mahesh will Gain Rs. 90 after 2 Years.

Answer 2

Answer:

$\huge\underline\mathbb\blue{SoLuTiOn:}$

At first,

Mahesh borrowed Rs.16000 at 7 1/2 or 7.5% .Time is 2 years.

☆Simple interest = Prn

$\implies$SI=16000 × 7.5% × 2

$\implies$SI =2400

★He has to give Rs.2400 as

simple interest.

Then, he lent Rs.16000 at 7.5% which was given as compound interest.Time is 2 years.

☆Compound Interest (CI)=P(1+r)^n-P

$\implies CI={16000(1+r)}^{n}-16000$

$\implies CI={16000(1+7.5\%)}^{2}-16000$

$\implies CI={16000(1+0.075)}^{2}-16000$

$\implies CI=16000\times{1.075}^{2}-16000$

$\implies CI=16000\times 1.155625-16000$

$\implies CI=18490-16000$

$\implies CI=2490$

So,he earned Rs.2490 as

compound interest.

So,Gain= CI-SI

Gain = 2490-2400

★ Gain = 90

$\large\boxed{Gain=Rs.90}$

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