Question

6) How much will Rs. 4000 amount to in 2 years at C.., if the rates of the
successive years be 5% and 8% respectively?​

Answer 1

Answer :

• Amount after 2 years, A = Rs. 4536

Explanation :

Given :

• Principal, P = Rs. 4000
• Time, T = 2 years
• Rate of interest, R1 = 5% p.a.
• Rate of interest, R2 = 8% p.a.

To find :

• Amount after 2 years, A = ?

Knowledge required :

Formula for amount (At successive rate of interests)

$\boxed{\sf{A = P\bigg(1 + \dfrac{R_{1}}{100}\bigg)\bigg(1 + \dfrac{R_{2}}{100}\bigg)\bigg(1 + \dfrac{R_{3}}{100}\bigg)...\bigg(1 + \dfrac{R_{n}}{100}\bigg)}}$

Where :

• A = Amount
• P = Principal
• R = Rate of interest

Solution :

By using the formula for amount for successive years, we get :

$:\implies \sf{A = P\bigg(1 + \dfrac{R_{1}}{100}\bigg)\bigg(1 + \dfrac{R_{2}}{100}\bigg)}$

$:\implies \sf{A = 4000 \times \bigg(1 + \dfrac{5}{100}\bigg)\bigg(1 + \dfrac{8}{100}\bigg)}$

$:\implies \sf{A = 4000 \times \bigg(\dfrac{100 + 5}{100}\bigg)\bigg(\dfrac{100 + 8}{100}\bigg)}$

$:\implies \sf{A = 4000 \times \bigg(\dfrac{105}{100}\bigg)\bigg(\dfrac{108}{100}\bigg)}$

$:\implies \sf{A = 4 \times \bigg(\dfrac{105}{10}\bigg) \times 108}$

$:\implies \sf{A = 4 \times \bigg(\dfrac{21}{2}\bigg) \times 108}$

$:\implies \sf{A = 2 \times 21 \times 108}$

$:\implies \sf{A = 4536}$

$\boxed{\therefore \sf{A = Rs. 4536}}$

Therefore,

• Amount after 2 years, A = Rs. 4536.

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

How much will Rs. 4000 amount to in 2 years at C , if the rates of the

successive years be 5% and 8% respectively?

$\huge{\boxed{\rm{\red{Answer}}}}$

$\large{\boxed{\sf{Given \: that}}}$

• Principal = Rupees 4000

• Time = 2 years

• Rate of interest { R1 } = 5 % Per annum [ P.A ] / Successive year's

• Rate of interest { R2 } = 8 % Per annum [ P.A ] / Successive year's

$\large{\boxed{\sf{To \: find}}}$

• Amount after 2 years.

$\large{\boxed{\sf{We \: also \: write \: as}}}$

• $\large\purple{\texttt{Principal as P}}$

• $\large\purple{\texttt{Time as T}}$

• $\large\purple{\texttt{Amount as A}}$

• $\large\purple{\texttt{Rate as R}}$

$\large{\boxed{\sf{Assumptions}}}$

• Rate of interest that is 5% as R1

• Rate of interest that is 8% as R2

$\large{\boxed{\sf{Solution}}}$

• Amount after 2 years = 4536 Rupees.

$\large{\boxed{\sf{Compulsory \: to \: know}}}$

• Formula of amount at successive { क्रमिक } amount is given below ↓

$a \: \: = \: \: p ( \: \: 1 \: + \frac{r1}{100} \: \: ) \: \: \: (1 + \frac{r2}{100} \: \: ) \: \: \: \: (1 + \frac{r3}{100} ) \: ..... \: \: \: (1 + \frac{rn}{100} )$

$\large{\boxed{\sf{Full \: solution}}}$

$\large\blue{\texttt{By using the formula of successive amount}}$

• a = p(1+R1) / 100 (1+R2) .

• A = 4000 × (1 + 5/ 100 ) (1 + 8/100 )

• A = 4000 × (100 + 5) / 100 (100 + 8) / 100

• A = 4000 × ( 105 / 100 ) ( 108 / 100 )

• A = 4 × ( 105 / 10 ) / 108

• A = 4 × (21/2) / 108

• A = 2 × 21 × 108

• A = 42 × 108

• A = 4536 Rupees.

$\bold{\pink{\fbox{\red{Hence, 4536 rupees is the amount}}}}$

$\bold{\pink{\fbox{\red{4536 rupees is the answer}}}}$

$\large{\boxed{\sf{Rupees \: 4536}}}$