Question

Find the amount and the compound interest on 2000 at 10% p.a. for 2 years, compounded annually
please don't use P (1+R/100) Formula​

Answer 1

Step-by-step explanation:

c.p=2000

r=10%

t=2years

c.p formula=p(1+r/100)

=2000(1+10/100)

=20(110/100)

=2200

Answer 2

Given :

• Principal (P) = Rs 2000
• Rate (R) = 10% p.a
• Time (T) = 2 years

To Find :

• Compound interest without the use of the Actual formula.

Solution :

✰ In this question, We have to find the Compound interest without using the formula. So firstly we will find the Interest for the First and Second Year separately after that we will substract the Total Amount and Principal to get the Compound interest. Now for finding the interest we will use P × R × T/100 and amount of first year will be taken as the principal for the second year as the interest is compounded annually.

⠀

• Principal for 1st year = Rs 2000
• Rate for 1st year = 10% p.a
• Time for 1st year = 1 year

⟶⠀Interest = P × R × T/100

⟶⠀Interest = 2000 × 10 × 1/100

⟶⠀Interest = 200 × 1

⟶⠀Interest = Rs 200

⠀

⟶⠀Amount = Interest + Principal

⟶⠀Amount = 200 + 2000

⟶⠀Amount = Rs 2200

⠀

So, Amount at the End of 1st year is ₹2200

___________________

✰ The Amount of the 1st will be taken as the Principal for the Second Year.

• Principal for 2nd year = Rs 2200
• Rate for 2nd year = 10% p.a
• Time for 2nd year = 1 year

⟶⠀Interest = P × R × T/100

⟶⠀Interest = 2200 × 10 × 1/100

⟶⠀Interest = 220 × 1

⟶⠀Interest = Rs 220

⠀

⟶⠀Amount = Interest + Principal

⟶⠀Amount = 220 + 2200

⟶⠀Amount = Rs 2420

⠀

So, Amount at the End of 2nd year is ₹2420

___________________

✰ Now, We know that Compound Interest is given by Amount - Principal. So let's find it.

⠀

⟶⠀Compound Interest = A - P

⟶⠀Compound Interest = 2420 - 2000

⟶⠀Compound Interest = Rs 420

⠀

Thus Compound Interest is Rs 420

___________________