Question

calculate the amount and compound interest on rupees 20000 for 3 years at 8% per annum using short method​

Answer 1

Answer:

★ Amount = Rs 25,194.24 ★

★ Compound Interest = Rs 5194.24 ★

Step-by-step explanation:

Given:

• Principal is Rs 20,000
• Time is 3 years
• Rate is 8% per annum

To Find:

• Amount at the end of 3 year and also Compound Interest

Solution:

† Simple Interest = P x R x T / 100

∴ S.I for 1st year = 20,000 x 8 x 1 / 100

$\small\implies{\sf }$ Rs 1600

∴ Amount at the end of 1st year = Principal + Amount at the end of 1st year

$\small\implies{\sf }$ 20,000 + 1600 = Rs 21,600 ( This amount will be principal for 2nd year )

Now, S.I for 2nd year = P x R x T / 100

∴ S.I for 2nd year = 21,600 x 8 x 1 / 100

$\small\implies{\sf }$ Rs 1728

∴ Amount at the end of 2nd year = 21,600 + 1728 = Rs 23,328 ( This amount will be principal for 3rd year)

Now, S.I for 3rd year = P x R x T / 100

∴ S.I for 3rd year = 23,328 x 8 x 1 / 100

$\small\implies{\sf }$ Rs 1866.24

∴ Final amount at the end of 3rd year = 23,328 + 1866.24 = Rs 25,194.24

Hence, The amount at the end of 3rd year = Rs 25,194.50

★ We know that Compound Interest = Amount – Principal

$\small\implies{\sf }$ C.I = Rs ( 25,194.50 – 20,000 ) = Rs 5194.24

Hence, The Compound Interest will be Rs 5194.24

__________________________________

★ Solving through another method ★

We know that the formula for finding Amount is

→ Amount = Principal ( 1 + r/100)^n

$\small\implies{\sf }$ A = 20,000 ( 1 + 8/100 )³

$\small\implies{\sf }$ A = 20,000 ( 108 / 100 )³

$\small\implies{\sf }$ A = 20,000 x 108/100 x 108/100 x 108/100

$\small\implies{\sf }$ A = 2 x 108 x 108 x 1.08

$\small\implies{\sf }$ A = Rs 25,194.24

Hence, Amount will be Rs 25,194.24

Therefore , C.I = A – P

→C.I = 25,194.24 – 20,000 =Rs5194.24