At what rate per cent per annum will 4000 amount to 4410 in 2 years when compounded annually

What will be the compound interest on 4000 at 5% per annum in two years.

Answer

Hint: Here we are given the principal amount of money, the rate of interest and it is to be compounded annually for 2 years. We will find out the compound interest using the formula. Consider all values given in question and try to identify which one to use where.
\[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\]
This will help in understanding the problem.

Complete step-by-step answer:
Here, we have the principal amount given (P) = 4000Rs.
The rate of interest per annum (r) = 5%
The total duration given is 2 years.
As we know, the formula of compound interest is
 \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\]
A is the total amount. R is rate of interest and P is the principal amount
Compounded for two years.
Given in the question, $ P = 4000Rs,r = 5\% ,n = 2years$
\[
  A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n} \\
   \Rightarrow A = 4000{\left( {1 + \dfrac{5}{{100}}} \right)^2} \\
   \Rightarrow A = 4000{\left( {1 + \dfrac{1}{{20}}} \right)^2} \;
 \]
Further, calculating the fraction we get
\[
   \Rightarrow A = 4000{\left( {\dfrac{{21}}{{20}}} \right)^2} \\
  Squaring\,bracket \\
   \Rightarrow A = 4000\left( {\dfrac{{441}}{{400}}} \right) \\
   \Rightarrow A = 4410Rs. \;
 \]
So, the amount after two years will be
 \[A = 4410Rs.\]
The compound interest will be
$
  Interest = Amount - Principal \\
   \Rightarrow Interest = 4410 - 4000 \\
   \Rightarrow Interest = 410\;Rs. \;
 $
So, the correct answer is “410 Rs.”.

Note: Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest

Get the answer to your homework problem.

Start your 7-day free trial and save 40% on your first month!

We don’t have your requested question, but here is a suggested video that might help.

Related Question

If $1000 is invested at 4% per annum compounded semiannually, how much is in the account after 2 years?

Discussion

You must be signed in to discuss.

Video Transcript

given the principle is $1000. The rate of interest is 4% 4 Annam interest being compounded semi annually, which means we're going toe half the rate of interest. So that will become 2% on the number of period of the turn. Your is off two years since it's been compounded semi and released. So the two nor will get doubled toe four years Now. We know that the amount on compound interest will be equal. Toe principal multiplied with one plus I divided by 100 raised to the power off in which will be equal to 1000 multiplied with one plus two divided by 100. Raise to the part of four which will be equal to 1000 multiplied with 1.2 raised to the power of full, which will give us the amount as equal toe 1082 point for $3 which is approximately equal to 1000 and $82

At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years

Question:

At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years when compounded annually?

Solution:

Let $R \% p . a .$ be the required rate.

$A=4410$

$P=4000$

$n=2$ years

Now,$A=\mathrm{P}\left(1+\frac{R}{100}\right)^{n}$

$\Rightarrow 4410=4000\left(1+\frac{\mathrm{R}}{100}\right)^{2}$

$\Rightarrow \frac{4410}{4000}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow \frac{441}{400}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow\left(\frac{21}{20}\right)^{2}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow \frac{21}{20}-1=\frac{R}{100}$

$\Rightarrow \frac{21-20}{20}=\frac{R}{100}$

$\Rightarrow \frac{1}{20}=\frac{R}{100}$

$\Rightarrow R=\left(\frac{1 \times 100}{20}\right)=5$

Hence, the required rate is $5 \%$ p.a.

At what rate percent will a sum of Rs 4000 amount to Rs 4410 in 2 years at compound interest?

At what rate of interest per annum would an amount $4000 yield a compound interest of?

In what time will 4000 amount to 4410 at 5% per annum compounded annually?

At what rate of interest will Rs 4000 amount to Rs 6000 in 2 years?