What is the compound interest on Rs 2000 for 2 years at the rate of interest 10% per annum?

(a) Rs 142.40

P = Rs 2000, r 1 = 4% p.a. for 1st year, r 2 = 3% p.a. for 2nd year

\(\therefore\) A = P\(\big(1+\frac{r_1}{100}\big)\big(1+\frac{r_2}{100}\big)\)

=2000\(\big(1+\frac{4}{100}\big)\big(1+\frac{3}{100}\big)\)

=Rs\(\big(2000\times\frac{26}{25}\times\frac{103}{100}\big)\)

= Rs 2142.40

\(\therefore\) C.I. = Rs 2142.40 – Rs 2000 = Rs 142.40.

Answer

Verified

Hint: To solve this type of problem, first calculate the final amount needed to pay after two year then subtract this final amount to the given principal amount to calculate the compound interest in two years.

Complete Step-by-step solution
Given principal amount is P =Rs 2000
Time to repay the amount is N = 2 years
Rate of interest is R =5 % per annum
To find the amount of compound interest after 2 years
C.I. = ?
To calculate the compound interest first we will calculate the final amount that we need to pay after 2 year
We know that the formula to calculate the final amount
$$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}$$
On putting the given values
$$A = 2000 \times {\left( {1 + \dfrac{{5}}{{100}}} \right)^2}$$
On simplification
$$A = 20000 \times \dfrac{{441}}{{400}}$$
$$A = 2205$$
Now we will calculate the compound interest
We know that
∴ $$C.I. = A - P$$
On putting the values of A and P
We get
$$ = Rs.2205 - Rs.2000$$
On subtracting
We get $$ = Rs.205$$

Hence the compound interest that needs to be paid after two year will be equal to Rs 205.

Note: The interest rate for the first year in compound interest is the same as that in case of simple interest, Other than the first year, the interest compounded annually is always greater than that in case of simple interest.
>When calculating compound interest, the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest.

At what rate percent per annum will a sum of Rs. 2000 amount to Rs. 2205 in 2 years, compounded annually ?

Answer

Verified

Hint: We have to only use the compound interest formula i.e. \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\], where A is the amount after T years, P is the principal amount, R is the rate of interest and T is the time period.Complete step-by-step solution -

As we know that the amount after two years will be equal to Rs. 2205.
The principal amount at the starting is equal to Rs. 2000.
And the time period is 2 years.
So, R be the rate of interest on which the principal amount is compounded annually.
So, now we can apply the formula of compound interest i.e. \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\] and then find the value of R by manipulating that equation.
So, putting values of A, P and T in the compound interest formula. We get,
\[2205 = 2000{\left( {1 + \dfrac{R}{{100}}} \right)^2}\]
Now dividing both sides of the above equation by 2000. We get,
\[\dfrac{{2205}}{{2000}} = {\left( {1 + \dfrac{R}{{100}}} \right)^2}\]
\[\dfrac{{441}}{{400}} = {\left( {1 + \dfrac{R}{{100}}} \right)^2}\]
Now taking the square root on both sides of the above equation. We get,
\[\sqrt {\dfrac{{441}}{{400}}} = \dfrac{{21}}{{20}} = \left( {1 + \dfrac{R}{{100}}} \right)\]
Now subtracting 1 to both sides of the above equation. We get,
\[\dfrac{{21}}{{20}} - 1 = \dfrac{1}{{20}} = \dfrac{R}{{100}}\]
On multiplying both sides of the above equation by 100. We get,
R = 5%
Hence, the rate of interest will be equal to 5%.

Note: Whenever we come up with this type of problem the we had to only use compound interest formula i.e. \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\] And after that dividing both sides of the equation by p and then taking square root to both the sides and after that subtracting 1 from both sides and multiplying by hundred. We will get the required value of R (i.e. rate of interest at which principal amount is compounded annually).

ML Aggarwal Solutions Class 9 Mathematics Solutions for Compound Interest Exercise 2.1 in Chapter 2 - Compound Interest

Question 9 Compound Interest Exercise 2.1

Find the amount and the compound interest on ₹ 2000 at 10% p.a. for 2 years, compounded annually.

Answer:

Compound interest is calculated on the principal as well as the interest earned over the preceding month. It differs from simple interest in that interest is not applied to the principal when computing the next period's interest.

It is given that

Principal (P) = ₹ 2000

Rate of interest (r) = 10% p.a.

Period (n) = 2 ½ years

We know that

Amount =\mathrm{P}(1+\mathrm{r} / 100)^{\mathrm{n}}

Substituting the values

=2000(1+10 / 100)^{2}(1+10 /(2 \times 100))

By further calculation

= 2000 × 11/10 × 11/10 × 21/20

So we get

= ₹ 2541

Here

Interest = A – P

Substituting the values

= 2541 – 2000

= ₹ 541

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