Answer  Hint: We need to find the knowledge about simple interest and compound interest. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments. The formula for the simple interest is $\text{Simple interest}\left( \text{S}\text{.I}\text{.} \right)\text{ = }\dfrac{P\times n\times r}{100}$ where P = principal value, n = number of years, r = the rate of interest. Compound interest is interest calculated on the initial principal which also includes all the accumulated interest from the previous periods. Complete step-by-step answer: The formula for compound interest is $A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$ where A = amount of previous value, P = principal value, n = number of years, r = the rate of interest.We need to understand the simple interest and compound interestSimple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.The formula for the simple interest is given as follows,$\text{Simple interest}\left( \text{S}\text{.I}\text{.} \right)\text{ = }\dfrac{P\times n\times r}{100}..................(i)$ ,where P = principal value, n = number of yearsr = the rate of interest.Compound interest is interest calculated on the initial principal which also includes all the accumulated interest from the previous periods.The formula for compound interest is as follows$A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}...........(ii)$ where A = amount of previous value,P = principal value, n = number of years,r = the rate of interest.Now, we need to find the simple interest and the compound interest of the situation we have been given,We have, P = Rs. 5000,n = 2 years,r = $6\%$,Substituting in the above equation we get,$\begin{align} & \text{Simple interest}\left( \text{S}\text{.I}\text{.} \right)\text{ = }\dfrac{5000\times 2\times 6}{100} \\ & =600 \end{align}$Therefore, the simple interest is Rs. 600.Now we need to substitute the same values in the formula for compound interest$A=5000{{\left( 1+\dfrac{6}{100} \right)}^{2}}$Solving the equation, we get,$\begin{align} & A=5000{{\left( 1.06 \right)}^{2}} \\ & =5000\times 1.1236 \\ & =5618 \end{align}$The compound interest is given by C.I. = Amount – principal amount.Therefore, by substituting the values, we get,C.I. = 5618 – 5000 = 618.Therefore, the compound interest is Rs. 618.We need to find the difference between simple interest and compound interest.The difference between simple and compound interest is 618 – 600 = RS. 18.Note: The answer we get from the compound interest formula is the amount and not the compound interest. We can find the compound interest by subtracting the principal from principal value. We do not need to worry about the sign while finding the difference between simple interest and compound interest.
100 Questions 100 Marks 90 Mins
Given: Principal = ₹5000 Rate of interest = 8% Time = 2 years Concept used: SI = (P × R × T)/100 CI = P × (1+ R/100)T – P Calculation: SI = (5000 × 8 × 2)/100 ⇒ SI = ₹800 CI = 5000 × (1 + 8/100)2 – 5000 ⇒ CI = ₹832 ⇒ CI – SI = ₹832 – ₹800 ∴ CI – SI is ₹32 Short trick: CI – SI for two years = P × (R/100)2 ⇒ CI – SI = 5000 × (8/100)2 ⇒ CI – SI = 5000 × 64/10000 ∴ CI – SI is ₹32India’s #1 Learning Platform Start Complete Exam Preparation
Daily Live MasterClasses
Practice Question Bank
Mock Tests & Quizzes Trusted by 3.3 Crore+ Students Find the difference between C.I and S.I on ₹ 5000 for 1 year at 2% p.a, if the interest is compounded half yearly Principal (P) = ₹ 5000 Time period (n) = 1 year Rate of interest (r) = 2% p.a For half-yearly r = 1% Difference between C.I and S.I is given by the formula C.I − S.I = `"P"("r"/100)^(2"n")` ...[For half yearly compounding] ∴ C.I − S.I = `5000(1/100)^(2 xx 1)` = `5000 xx 1/100 xx 1/100` = ₹ 0.50 Concept: Difference Between Compound Interest and Simple Interest Is there an error in this question or solution? |
What is the difference between CI and S.I on 5000?
Pos Terkait
Copyright © 2024 ketajaman Inc.
