On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to Rs. 63 ?A. Rs. 24600 Show
B. Rs. 24800 C. Rs. 25200 D. Rs. 25500 Answer: Option C Solution(By Examveda Team)$$\eqalign{ & {\text{Rate of interest = 5}}\% {\text{ per annum}} \cr & {\text{Time = 2 year}} \cr & {\text{Accroding to question,}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{r}{{100}}} \right)}^n} - 1} \right] - \frac{{P \times r \times t}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{P \times 5 \times 2}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {\frac{{105}}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left( {\frac{{11025 - 10000}}{{10000}}} \right) - \frac{{10P}}{{100}} = 63 \cr & \Rightarrow \frac{{1025P}}{{10000}} - \frac{{10P}}{{100}} = 63 \cr & \Rightarrow \frac{{1025P - 1000P}}{{10000}} = 63 \cr & \Rightarrow 25P = Rs.630000 \cr & \Rightarrow P = \frac{{630000}}{{25}} \cr & \Rightarrow P = Rs. 25200 \cr & {\text{Hence}},\,{\text{sum Rs}}{\text{. 25200}} \cr} $$ Click here to read 1000+ Related Questions on Compound Interest(Arithmetic Ability)On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.? SolutionC.I = `P[(1 + r/100)^2 - 1] = P[(1 + 5/100)^2 - 1] = "41P"/400` `S.I = (P xx 5 xx 2)/100 = P/100` Given, C.I. - S.I. Rs. 25 `=> "41P"/400 - P/10 = 25` `=> (41P - 40P)/400 = 25` `=> P = 10000` ∴ Required sum = Rs. 10,000 Concept: Concept of Compound Interest - Compound Interest as a Repeated Simple Interest Computation with a Growing Principal Is there an error in this question or solution? APPEARS INOn what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to Rs. 63/-
Answer (Detailed Solution Below)Option 3 : Rs. 25200/- Free Territorial Army Paper I - Full Mock Test 100 Questions 100 Marks 120 Mins Given: Time is 2 years Rate is 5% per annum The difference between simple interest and compound interest is Rs. 63. Concept: S.I = (P × R × T)/100 C.I = P[(1 + r/100)n - 1] Here, n is the number of terms in the year Calculation: Let sum be Rs. P Now, The simple interest for 2 years at 5% per annum is (P × 5 × 2)/100 ⇒ P/10 Now, The compound interest for 2 years at 5% per annum is P[(1 + 5/100)2 - 1] ⇒ P[(21/20)2 - 1] ⇒ P[(441/400) - 1] ⇒ 41P/400 So, The difference between Compound interest and simple interest is ⇒ 41p/400 - P/10 = 63 ⇒ 41P - 40P = 63 × 400 ⇒ P = Rs. 25200 ∴ The required sum of money is Rs. 25200.
The difference between compound interest and simple interest for 2 years is ⇒ P(r/100)2 According to question ⇒ P(5/100)2 = 63 ⇒ P × 1/400 = 63 ⇒ P = 63 × 400 ⇒ P = 25200 ∴ The required sum of money is Rs. 25200 Latest Territorial Army Updates Last updated on Sep 22, 2022 The Territorial Army has released the official notification for Territorial Army Exam 2022. Through this exam, Territorial Army Officers will be recruited to serve as the secondary defense force of the nation. The candidates must note that this is not a regular Indian Army job. This is a part-time commitment for serving the nation. The exam is scheduled to be held on 25th September 2022. The candidates must go through the Territorial Army Exam Preparation Tips which will help the candidates to make a better strategy to clear the exam. Let's discuss the concepts related to Interest and Simple and Compound Both. Explore more from Quantitative Aptitude here. Learn now! For what sum of money the difference between simple interest and compound interest for 2 years at 5% per annum equals to Rs 50?Hence, the sum is Rs. 6000.
On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to 63?The difference between simple interest and compound interest is Rs. 63. ∴ The required sum of money is Rs. 25200.
On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum is rupees 12 find the sum of money?This is Expert Verified Answer
And based on a two-year compounded interest rate and the rate of %. Hence, the required answer is Rs. 20,000.
On what sum will the compound interest at 5% per annum for 2 years compounded annually be Rs 1647?On what sum will the compound interest at 5% per annum for 2 years compounded annually be ₹164. The required sum is ₹1600.
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On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum?
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