Question

An amount of rs. 10,000 becomes rs. 20,736 in 2 years. If the rate of interest is compounded half yearly, what is the annual rate of interest

Answer 1

Answer:

20% interest half yearly.

40% interest yearly.

Step-by-step explanation:

principal = 10000

amount = 20736

time = 2 years

half yearly means 4 times.

let, rate of interest = r

formula

$p {(1 + \frac{r}{100}) }^{4} = amount \\ or \: 10000 \times \frac{ {(100 + r)}^{4} }{100000000} = 20736 \\ or \: {(100 + r)}^{4} = 207360000 \\ or \: 100 + r = 120 \\ or \: r = 20$

Answer 2

Concept Introduction:-

It may be in the form of a word, a symbol, or a figure that reflects the arithmetic value of a quantity.

Given Information:-

We have been given that an amount of rs. $10,000$ becomes rs. $20,736$ in $2$ years.

To Find:-

We have to find that the annual rate of interest.

Solution:-

According to the problem

principal$= 10000$

amount $= 20736$

time$= 2 years$

half yearly means $4$ times.

let, rate of interest = r

formula

$p(1+\frac{r}{100})^4=amount\\10000\frac{(1+{r^4)}}{100000000}=20736\\(100+r)^4=207360000\\100+r=120\\r=120-100\\=20\%$

Final Answer:-

The annual rate of interest is $20\%$.

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