What will be the compound interest on rupees 20000 at the rate of 5% per annum for 2 years?

Find the compound interest on Rs. 20,000 for 2 years, compounded annually at 10% per annum.A) 4200B) 4300C) 4400D) 4500

Answer

Verified

Hint: 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 answer:
Given principal amount is
 P=Rs 20000
Time to repay the amount is
T= 2 years
Rate of interest is
R=10% 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
$$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$$
On putting the given values
$$A = 20000 \times {\left( {1 + \dfrac{{10}}{{100}}} \right)^2}$$
On simplification

$$A = 20000 \times \dfrac{{121}}{{100}}$$
Now we will calculate the compound interest
We know that

∴ $$C.I. = A - P$$
On putting the values of A and P
We get
$$ = Rs.24,200 - Rs.20,000$$
On subtracting
We get
$$ = Rs.4200.$$

Hence the compound interest that I need to pay after two year will be equal to Rs 4200.
Therefore the correct option is ‘A’

Additional information: 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.

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.

Jump to

• Compound Interest Exercise 14.1
• Compound Interest Exercise 14.2
• Compound Interest Exercise 14.3
• Compound Interest Exercise 14.4
• Compound Interest Exercise 14.5

• Rational Numbers
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• Playing with Numbers
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• Linear Equation in One Variable
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• Time and Work
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• Compound Interest
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RD Sharma Solutions Class 8 Mathematics Solutions for Compound Interest Exercise 14.1 in Chapter 14 - Compound Interest

Question 8 Compound Interest Exercise 14.1

Mewa lal borrowed Rs. 20000 from his friend Rooplal at 18% per annum simpleinterest. He lent it to Rampal at the same rate but compounded annually. Find hisgain after 2 years.

Answer:

Given details are,

Principal (p) = Rs 20000

Rate (r) = 18 %

Time = 2 years

By using the formula,

Interest amount Mewa lal has to pay,

By using the formula,

Simple interest = P×T×R/100

= (20000×18×2)/100 = 7200

Interest amount Rampal has to pay to Mewa lal,

By using the formula,

A = P (1 + R/100)^n

= 20000 (1 + 18/100)^2

= 20000 (118/100)^2

= Rs 27848 – 20000 (principal amount)

= Rs 7848

∴ Mewa lal gain = Rs (7848 - 7200) = Rs 648

Video transcript

hello students welcome to lero's question and answer classroom my name is shaista firozi class and today let's see what are we going to find out okay so let's start with the question what the question says the question says borrowed rupees twenty thousand so my principal amount is twenty thousand which miwa lal is borrowing from his friend ruplan so mevalal is borrowing from rupal 20 000 rupees which are principal amount at 18 percent per annum simple interest okay so here you can see that here it is by simple interest rupal is giving new alarm 20 000 rupees at 18 per annum he lent it to ram pal at the same rate so ruplal is again lending it to rampal but at the same rate but compounded annually so here you are going to find out the compound interest because he is giving it with the same rate but annually compounding annually so compound interest find his gain after two years so our time period is given as two years so let's quickly jot down whatever details are being provided to us so the details are the principal amount principle is rupees 20 000 okay at 18 per annum so my rate of interest is 18 and my period that is time or you can say n is two years okay so now let's quickly start because it was specified that here uh maevalal is borrowing this amount from the friend rupal for with simple interest so let's quickly find out first simple interest so my simple interest would be before that i would write down for your information that this is the interest or you can say the simple interest amount has to pay to ruply okay so let's find out what is miwalal going to pay to rupal the simple interest so my simple interest formula is equals to principal into rate of interest into time upon 100 so my principle as you all know that it is 20 000 into my rate of interest which is 18 into time which is 2 years upon 100 so on calculation the ho calculating the whole thing i am going to get my simple interest as rupees seven thousand two hundred so i have received the simple interest which malala is going to pay to rupal now he is he has lent it to rampal but with compound interest so let's quickly find out the compound interest also because it's the same rate of interest okay so i am going to write down the formula for compound interest first so my compound interest is equals to amount minus principle but i know that i don't have the amount so let's quickly first find out the amount for this so my amount formula as you all know that it is principal that is p 1 plus my rate of interest that is r upon 100 raised to n so my principle is given as 20 000 1 plus my rate of interest is 18 upon 100 raised to n which is two years so now i am going to do is i am going to simplify this whole bracket by taking an lcm which is 100 as an lcm i will take it and i will solve this whole bracket so let's see i get twenty thousand one plus sorry uh it will be hundred and eighteen upon hundred so hundred and eighteen upon 100 raised to 2 okay so this is my power now i am going to solve this that is i'm going to take the square of 118 and 100 i'm going to multiply i'm going to divide this and multiply by 20 with 20 000 and i am going to get my amount as rupees 27 848 on solving the whole brackets and 20 000. so this is what i have received my amount now let's quickly substitute this amount in the formula of compound interest so now as you all know that my compound interest is equals to amount minus principle my amount is 27 848 so i'm writing 27 848 minus my principle my principal is 20 000 so i'm going to subtract this on subtracting this i am going to get my compound interest as 7848 so we have got our compound interest we have got a simple interest now since it says that you have to find what uh what was his gain okay so let's write down or quickly find out what did he gain from this okay so let's write down mewalal what did mewalal gain so mevalal gain is nothing but simple interest as well as our compoundedness so i'm just going to subtract this so mevala gain would be equals to and forty 7848 minus seven thousand two hundred rupees which is nothing but equal to rupees six hundred and forty eight rupees so please uh as you know that if it was to find out his gain after two years so you can write on that after two years maywalal gain is nothing but rupees 604 which is our answer so please note down our answer is rupees 648 so all right that's our answer subscribe to lido for more updates and do comment don't forget to update and don't forget to comment see you all next time bye bye take care

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