Question

4. How much will $20,000 amount to in 2 years
at CI if the rates for successive years are 8%
and 10% p.a. respectively?​

Answer 1

Step-by-step explanation:

Principal = $20,000

Time = 2 years

R(1) = 8%

R(2) = 10%

Amount

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

$= 20000(1 + \frac{8}{100})(1 + \frac{10}{100} ) \\ = 20000(1 + \frac{2}{25})( 1 + \frac{1}{10}) \\ = 20000 \times \frac{27}{25} \times \frac{11}{10} \\ = 80 \times 27 \times 11 \\ = 23,760$

Om Namah Shivaya

Debasish Biswal

Answer 2

Given :-

Principal = $20,000

Time = 2 years

Rate for the first year = 8%

Rate for the second year = 10%

To Find :-

The compound interest

Solution :-

For the first year :-

Principal = $20,000

Time = 1 year

Rate = 8%

$Interest\: =\: {\dfrac{P \times R \times T}{100}}$

On inserting the values in the formula

We get ,

$Interest\: =\: {\dfrac{20000 \times 8 \times 1}{100}}$

$\implies\: Interest\: =\: {\dfrac{\cancel{20000}^{200}\: \times 8 \times 1}{\cancel{100}^{1}}}$

$\implies\: Interest\: =\: \bold{1600}$

Amount = Principal + Interest

= $ 20,000 + $ 1,600

= $ 21,600

For the second year :-

Principal = $ 21,600

Time = 1 year

Rate = 10%

$Interest\: =\: {\dfrac{P \times R \times T}{100}}$

On inserting the values in the formula

On inserting the values in the formulaWe get ,

$\implies\: Interest\: =\: {\dfrac{21600 \times 10 \times 1}{100}}$

$\implies\: Interest\: =\: \bold{2160}$

Amount = Principal + Interest

= $ 21,600 + $ 2,160

= $ 23,760

Compound Interest = Final Amount - Original Principal

= $ 23,760 - 20,000

= $ 3,760

Therefore, compound interest is $ 3,760