Question

Simple interest on a certain sum of money at 9% is ₹450 in 2 years. Find the compound interest, on the same sum. at the same rate for 1 year, if the interest is reckoned half yearly. The answer is 227.25 but my answer is 230.0625. Please help

Answer 1

Answer:

The compound interest for the same principal sum is Rs 230.06

Step-by-step explanation:

Given as :

The simple interest on certain sum = s.i = Rs 450

The time period = t = 2 years

The rate of interest = r = 9 %

Let The principal sum = Rs p

According to question

From Simple Interest method

Simple interest = $\dfrac{\textrm principal\times \tetxrm rate\times \textrm time}{100}$

i.e s.i = $\dfrac{\textrm p\times \tetxrm r\times \textrm t}{100}$

Or, Rs 450 = $\dfrac{\textrm p\times \tetxrm 9\times \textrm 2}{100}$

Or, 18 × p = 45000

∴  p = $\dfrac{45000}{18}$

i.e p = Rs 2500

So, The principal sum amount = p = Rs 2500

Again

At The The principal sum amount = p = Rs 2500

The rate of interest = R = 9%  half yearly

The time period = T = 1 year

Let The Amount after 1 year = Rs A

Let The compound interest = c.i

From Compound Interest method

Amount = principal × $(1+\dfrac{\textrm rate}{2\times 100})^{\textrm 2\times time}$

Or, A = p × $(1+\dfrac{\textrm R}{2\times 100})^{\textrm 2\times T}$

Or, A = 2500 × $(1+\dfrac{\textrm 9}{2\times 100})^{\textrm 2\times 1}$

Or, A = 2500 × (1.045)²

Or, A = 2500 × 1.092005

Or, Amount = Rs 2730.06

∵, The compound interest = Amount - principal

Or, c.i = A - P

Or, c.i = Rs 2730.06 - Rs 2500

∴  c.i = Rs 230.06

Hence, The compound interest for the same principal sum is Rs 230.06 Answer

Answer 2

Answer:

I had the same issue. It is typing error