On what sum will compound interest at 5% per annum for 2 years compounded annually be rupees 164?

Question 1 Compound Interest Exercise 14.3

Answer:

Given details are,Rate = 5 % per annum

Compound Interest (CI) = Rs 164

Time (t) = 2 years

By using the formula,

Let P be ‘x’

CI = A – P

164 = P (1 + R/100)*n – P

= P [(1 + R/100)^n - 1]

= x [(1 + 5/100)^2 – 1]

= x [(105/100)^2 – 1]

164 = x ((1.05)^2 – 1)

x = 164 / ((1.05)^2 – 1)

= 164/0.1025

= Rs 1600

∴ The required sum is Rs 1600

Video transcript

hello students welcome to lido's question and answer classroom my name is shaista firozi class and today we are going to find out the sum okay so before we find out the sum let's see what the question says and the question is on what sum will the compound interest at five percent per annum for two years compounded annually b rupees 164. so that means this is clear that we need to find out the sum for the compound interest at five percent per nm so rate is five percent then time is for two years and my compound interest is rupees 164. so let's quickly jot down the details given to us so my rate is five percent for two years so that means my time period n is two years and my compound interest is rupees 160 i want to find out my sum or i can say principle so let this be p now let's quickly write down the formula for this so my formula for this is compound interest would be just hold on i'll just clear the screen so my compound interest formula as you know that it is amount minus principle so what i am going to do is i'm going to apply the formula over here in amount because i don't have an amount also and i don't have a principle also so i'll apply the formula of amount over here and i'll write down the formula instead of a that is amount so let's write down it will be compound interest is equals to now amount i don't know so i'll just write down the formula for amount which is p 1 plus r upon 100 raised to n minus p so my compound interest is 164. my principle i don't know that is supposed to be p 1 plus rate of interest is 5 raised to 2 years minus 1 okay now we have written this we will quickly change into decimal form so i'm going to change this particular part into the decimal form so let's write down this as p 1 plus 0.05 raised to 2 minus 1 becomes 164 is equals to p 1.05 raised to 2 minus 1 so 164 is equals to p into 1.05 raise to 2 minus 1 would give you 0.1025 okay so this becomes 164 upon 0.1025 is equals to p okay now just hold on i'll write down the calculation once the calculation is done so now i am going to write down my sum that is p would be after i have solved this that is after i have divided 164 by 0.1025 i will get my sum as 1600 rupees okay so this is my principle so this would be the required sum is rupees 1600 this is what the answer is okay that's all for today see you all next time till then please subscribe to lido and do comments don't forget to comment and subscribe bye bye take care