Question

calculate the amount and compound interest on 20000 for 3 years if the interest compound annually and the rate of interest is 5% of the first year 7% for the second year and 9% the third year​

Answer 1

$\huge\textsf{Question:-}$

Calculate the amount and compound interest on Rs. 20000 for 3 years if the interest is compounded annually and the rate of interest is 5% for the first year, 7% for the second year, and 9% the third year.

$\huge\textsf{Solution:-}$

$\blue{Method\: 1:Without\: using\: formula}$

1st year,

Principal(p) = Rs. 20000

rate(r) = 5%

time (t)=1 year

Interest (i) = $\frac{p \times r \times t}{100}$

$= Rs. \frac{20000 \times 5 \times 1}{100} \\ \\ =Rs. 1000$

Therefore,

Amount = p+i

= Rs. (20000 + 1000)

= Rs. 21000

2nd year,

Principal(p) = Rs. 21000

rate(r) = 7%

time (t)=1 year

Interest (i) = $\frac {p \times r \times t}{100}$

=Rs. $\frac {21000\times 7 \times 1}{100}$

= $Rs. 1470$

Therefore,

Amount = p+i

= Rs. (21000 + 1470)

= Rs. 22470

3rd year,

Principal(p) = Rs. 22470

rate(r) = 9%

time (t)=1 year

Interest (i) = $\frac {p \times r \times t}{100}$

=Rs. $\frac {22470\times 9\times 1}{100}$

= Rs. $2046.6$

Therefore,

Amount = p+i

= Rs. (22470 + 2046.6)

= Rs. 24516.6

$\textbf{Answer:-}$

Amount after 3 years = Rs. 24516.6

Compound Interest after 3 years = Final amount - original principal

= Rs. (24516.6 - 20000)

= Rs. 4516.6
______________________________

$\blue{Method\: 2: Using\:formula}$

Principal = Rs. 20000

rate 1 = 5%

rate 2 = 7%

rate 3 = 9%

time = 3 years

$\textbf{Answer:-}$

Amount = p( 1+ $\frac{r1}{100}$)(1+ $\frac{r2}{100}$)(1+ $\frac{r3}{100}$)

= Rs. 20000 ( 1+ $\frac{5}{100}$)(1+ $\frac{7}{100}$)(1+ $\frac{9}{100}$)

= Rs. 20000($\frac{100 + 5}{100}$)($\frac{100+7}{100}$)( $\frac{100+9}{100}$)

= Rs. 20000 × $\frac {105}{100}$ × $\frac {107}{100}$ × $\frac {109}{100}$

=Rs. 24516.6

Compound Interest = Amount - Principal

= Rs. (24516.6 - 20000)

= Rs. 4516.6

Answer 2

Answer:

4516.5

Step-by-step explanation:

1st year,

Principal(p) = Rs. 20000

rate(r) = 5%

time (t)=1 year

Interest (i) =  

Therefore,

Amount = p+i

= Rs. (20000 + 1000)

= Rs. 21000

2nd year,

Principal(p) = Rs. 21000

rate(r) = 7%

time (t)=1 year

Interest (i) =  

=Rs.  

=  

Therefore,

Amount = p+i

= Rs. (21000 + 1470)

= Rs. 22470

3rd year,

Principal(p) = Rs. 22470

rate(r) = 9%

time (t)=1 year

Interest (i) =  

=Rs.  

= Rs.  

Therefore,

Amount = p+i

= Rs. (22470 + 2046.6)

= Rs. 24516.6

Amount after 3 years = Rs. 24516.6

Compound Interest after 3 years = Final amount - original principal

= Rs. (24516.6 - 20000)

= Rs. 4516.6

______________________________

Principal = Rs. 20000

rate 1 = 5%

rate 2 = 7%

rate 3 = 9%

time = 3 years

Amount = p( 1+ )(1+ )(1+ )

= Rs. 20000 ( 1+ )(1+ )(1+ )

= Rs. 20000()()( )

= Rs. 20000 ×  ×  ×  

=Rs. 24516.6

Compound Interest = Amount - Principal

= Rs. (24516.6 - 20000)

= Rs. 4516.6