What is the compound interest on Rs 50000 for 4 %per annum for 2 years compounded annually?

Solution:

The expression which helps determining compound interest is:

A = P(1 + r/100)n

And

Compound Interest (CI) = A - P

Where,

A = Amount at the end of the designated period

P = principal

r = rate of interest compounded annually

n = time period

P = Rs. 50, 000

r = 4% compounded annually

n = 2 years

Therefore we can write:

A = 50,000(1 + 4/100)2

= 50,000(1.04)2

= 50,000(1.0816)

= 54,080

Hence,

CI = 54,080 - 50,000

CI = Rs. 4,080

✦ Try This: The compound interest on Rs 50,000 at 8% per annum for 1 years compounded semi-annually is (a) Rs 4,000, (b) Rs 4,080, (c) Rs 4,280, (d) Rs 4,050

Since,

A = P[1 + (r/2)(1/100)]n

= P[1 + (r/200)]n

= 50,000[1 + (8/200)]2

= 50,000[1 + 0.04]2

= 50,000[1.04]2

= 50,000[1.0816]

= 54,080

CI = 54,080 - 50,000

= Rs.4,080

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 8

NCERT Exemplar Class 8 Maths Chapter 9 Problem 3

The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is (a) Rs 4,000, (b) Rs 4,080, (c) Rs 4,280, (d) Rs 4,050

Summary:

The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is Rs.4080

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The compound interest on Rs. 50,000 at 4% per annum for two years compounded annually is:1) 40002) 40803) 42804) 4050

Answer

Verified

Hint: We have to find out how much Rs. 50,000 will amount to after two years if the rate of interest is given as 10% and interest is compounded annually. For this question our principal amount will be Rs. 50,000, the rate of interest will be 4% and time is 2 years. Substitute these values in the direct formula for compound interest.

Complete step-by-step answer:
We are given that the amount is Rs. 50,000 on which interest will be paid.
The amount 50,000 is our principal amount $P$.
Now, we are also given that the rate of interest is 4% which is denoted by $r$.
The time-period $\left( T \right)$ for which compound interest should be calculated is given as 2 years.
As, we know that the compound interest is calculated using the formula, $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^T}$, where \[A\] is the total amount, $P$ is the principal amount, $r$ is the rate of interest and $T$ is the time-period.
On substituting the value, we get,
$
  A = 50,000{\left( {1 + \dfrac{4}{{100}}} \right)^2} \\
  A = 50,000{\left( {\dfrac{{104}}{{100}}} \right)^2} \\
  A = 50,000\left( {\dfrac{{104}}{{100}}} \right)\left( {\dfrac{{104}}{{100}}} \right) \\
  A = 5\left( {104} \right)\left( {104} \right) \\
$
Therefore, on solving we get,
$A = 54,080$
Now, we will calculate the interest by subtracting the principal amount from the total amount.
$C.I. = A - P$, where C.I. stands for compound interest.
Therefore,
 $
  C.I. = 54,080 - 50,000 \\
  C.I. = 4,080 \\
 $
Hence, option B is correct.

Note: Make sure the time period that is given in the question is in years, and if it is given in months one must convert it to years. Whenever we are given to calculate the compound interest, we first calculate the total amount and then subtract the principal amount from it.

Question

The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually in rupees is

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Solution

The correct option is B 4,080Given, P = Rs. 50000, R = 4%, T = 2 years A=P(1+R100)T=50000(1+4100)2=50000(2625)2=54080 Compound interest = A - P = 54080 - 50000 = 4080

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