Question

$\large{\blue{\maltese \: \: {\pink{\underbrace{\underline{\red{\pmb{\sf{  Question :-}}}}}}}}}$
Find the amount and the compound interest on ₹ 12,000 in 3 years, when the rates of interest for successive years are 10%, 12% and 15% respectively. ​

Answer 1

Answer:

Given :-

• A sum of Rs 12000 in 3 years, when the rates of interest for successive years are 10%, 12% and 15% respectively.

To Find :-

• What is the amount and compound interest.

Formula Used :-

$\clubsuit$ Amount Formula :

$\longrightarrow \sf\boxed{\bold{\pink{A =\: P\bigg(1 + \dfrac{r_1}{100}\bigg) \bigg(1 + \dfrac{r_2}{100}\bigg) \bigg(1 + \dfrac{r_3}{100}\bigg)}}}$

where,

• A = Amount
• P = Principal
• $\sf r_1$ = Rate of Interest for first year
• $\sf r_2$ = Rate of Interest for second year
• $\sf r_3$ = Rate of Interest for third year

$\bigstar$ Compound Interest or C.I Formula :

$\dashrightarrow \sf\boxed{\bold{\pink{Compound\: Interest =\: A - P}}}$

where,

• A = Amount
• P = Principal

Solution :-

Given :

• Principal = Rs 12000
• Rate of Interest = 10%, 12% and 15%
• Time Period = 3 years

According to the question by using the formula we get,

$\small \implies \sf A =\: 12000\bigg(1 + \dfrac{10}{100}\bigg) \bigg(1 + \dfrac{12}{100}\bigg) \bigg(1 + \dfrac{15}{100}\bigg)$

$\small \implies \sf A =\: 12000\bigg(\dfrac{100 + 10}{100}\bigg) \bigg(\dfrac{100 + 12}{100}\bigg) \bigg(\dfrac{100 + 15}{100}\bigg)$

$\small \implies \sf A =\: 12000\bigg(\dfrac{110}{100}\bigg) \bigg(\dfrac{112}{100}\bigg) \bigg(\dfrac{115}{100}\bigg)$

$\small \implies \sf A =\: 12000 \times \dfrac{110}{100} \times \dfrac{112}{100} \times \dfrac{115}{100}$

$\small \implies \sf A =\: 12{\cancel{000}} \times \dfrac{1416800}{1000\cancel{000}}$

$\small \implies \sf A =\: 12 \times \dfrac{14168\cancel{00}}{10\cancel{00}}$

$\small \implies \sf A =\: 12 \times \dfrac{14168}{10}$

$\small \implies \sf A =\: \dfrac{12 \times 14168}{10}$

$\small \implies \sf A =\: \dfrac{170016}{10}$

$\small \implies \sf\bold{\purple{A =\: Rs\: 17001.60}}$

$\therefore$ The amount is Rs 17001.60 .

Now, we have to find the compound interest :

Given :

• Amount = Rs 17001.60
• Principal = Rs 12000

According to the question by using the formula we get,

$\mapsto \sf Compound\: Interest =\: Rs\: 17001.60 - Rs\: 12000$

$\mapsto \sf\bold{\red{Compound\: Interest =\: Rs\: 5001.60}}$

$\therefore$ The compound interest is Rs 5001.60 .

Answer 2

Principal (P) = ₹ 10,000

Time (t) = 3 Years

Rate = (R1) = 10%

Rate = (R2) = 15%

Rate = (R3) = 20%

Amount = P (1 + (R1/100)) (1 + (R2/100)) (1 + (R3/100))

= ₹ 10,000 × (1 + (10/100)) (1 + (15/100)) (1 + (20/100))

= ₹10,000 × 11/10 × 23/20 × 6/5 = ₹15,180

C.I. = Amount – Principal

= ₹ 15,180 - ₹10,000 = ₹5180