Question

3. A sum of Rs 30,000 is invested for 3 years at 15/2% p.a. compound interest.

(i) What is the sum at the end of the second year?

(ii) What is the sum at the end of the 3 years?

(iii) What is the total interest earned in 3 years?​

Answer 1

Answer:

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Answer 2

$\overline{ \underline{ \boxed{ \sf GIVEN \darr}}}$

A sum of Rs 30,000 is invested for 3 years at 15/2% p.a. compound interest.

(i) What is the sum at the end of the second year?

(ii) What is the sum at the end of the 3 years?

(iii) What is the total interest earned in 3 years?

$\overline{ \underline{ \boxed{ \sf HOW \: TO \: DO \darr}}}$

For (I)

Step 1 : First we will calculate the Interest of the first year

Step 2 : Then the amount of first year Interest for 1st year added with principal

Step 3 : Then the amount for 1st yr will principal for 2nd year.

For (ii)

Step 1 : Do the same way as we did for part-1

Step 2 : Then add the Interest with the principal to get the amount

For (iii)

Step 1 : Substract the principal from the amount to the get the Compound Interest

$\overline{ \underline{ \boxed{ \sf SOLUTION \darr}}}$

I) According to steps we will find the result of part-1

Interest for the first year = P × R × T/100

Here,

P is Principal which is ₹ 30000

T is time which is 1 year

R is Rate of Interest which is 15/2

Putting the values we get

$\frak{Interest = \frac{30000 \times \frac{15}{2} \times 1}{100} }$

$\frak{Interest = \frac{15000 \times 15 \times 1}{100} }$

$\frak{Interest = \frac{2250 \cancel{00}}{1 \cancel{00}} }$

$\green{ \boxed{ \frak{ \red{Interest \: for \: {1}^{st} \: year \: is \: rs.2250} }}}$

So

amount after one year = Interest + Principal

= ₹ 2250 + ₹ 30000

= ₹ 32250

Amount is ₹ 32250

Principal for the second year is ₹ 32250

Time is 1 year

Rate of Interest is 15/2

Interest for the second year = P × R × T/100

$\frak{Interest = \frac{32250 \times \frac{15}{2} \times 1}{100} }$

$\frak{Interest = \frac{16125 \times 15 \times 1}{100} }$

$\frak{Interest = \frac{241875}{100 }}$

$\purple{ \boxed{ \frak{ \blue{Interest \: for \: {2}^{nd} \: year \: is \: rs \: 2418.75} }}}$

So

amount after 2nd year = Interest + Principal

= ₹ 2418.75 + ₹ 32250

= ₹ 34668.75

Hence, the amount at the end of 2 years is ₹ 34668.75

ii) Principal is ₹ 30000

Time is 3 years

Rate of Interest is 15/2

Using formula

$\sf A = P(1 + \frac{r}{100} )^{n}$

Here, n is time

Putting the values we get

$\sf A = 30000(1 + \frac{ \frac{15}{2} }{100} )^{3}$

$\sf A = 30000(1 + \frac{3}{40} )^{3}$

$\sf A = 30000 \times (\frac{43}{40})^{3}$

$\sf A = 30 \cancel{000} \times \frac{79507}{64 \cancel{000}}$

$\sf A= 37268.9$

Therefore, the amount after 2 years is ₹ 37268.9

iii) Now to find the interest in three years

Using formula

Compound Interest = Amount - Principal

Compound Interest = ₹ 37268.9 - ₹ 30000

Compound Interest = ₹ 7268.9

Hence, the interest after 3 years is ₹ 7268.9

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