Find the rate at which a sum of money will become four times the original amount in 2 years, if the interest is compounded half-yearly. Show
SolutionLet the rate percent per annum be R. Concept: Rate Compounded Annually Or Half Yearly (Semi Annually) Is there an error in this question or solution? APPEARS INGiven details are, Time = 2 years = 2×2 = 4 half years Let rate = R % per annum = R/2% half years Let principal be = P So, Amount becomes = 4P By using the formula, A = P (1 + R/100)n 4P = P (1 + R/2×100)4 (1 + R/200)4 = 4 (1 + R/200) = 41/4 1 + R/200 = 1.4142 R/200 = 1.4142-1 = 0.4142 R = 0.4142 × 200 = 82.84% ∴ Required Rate is 82.84% per annum. A sum of money becomes 4 times of itself in 4 year at compound interest, then find in how many years this sum becomes 16 times at the same rate of interest?
Answer (Detailed Solution Below)Option 3 : 8 Free RRB Group D: Memory Based Question Full Test based on 17 Aug 2022 100 Questions 100 Marks 90 Mins Given: A sum become 4 times itself in four years Formula used: A = P(1 + r/100)t Where A is amount r is rate of interest t is time taken Calculation: Let amount be 16 times in t years According to the question 4P = P(1 + R/100)4 ----(1) 16P = P(1 + R/100)t ----(2) From equation (1), we get ⇒ (1 + R/100) = √2 From equation (2), we get ⇒ 16 = √2t ⇒ 24 = √2t ⇒ 4 = t/2 ⇒ 8 = t ∴ In 8 years the amount become 16 times  The amount increase in G.P in case of compound interest P becomes 4 times itself in 4 years After 4 years principal become 4P ⇒ 4P becomes 4 times itself after then it becomes 16P ∴ In 8 years the amount become 16 times Latest RRB Group D Updates Last updated on Sep 27, 2022 The Railway Recruitment Board has released RRB Group D Phase 5 Admit Card. The exam will be conducted on 6th and 11th October 2022 only for the RRC South Western Railway. Currently, the Phase 4 is running and this will continue till 7th October 2022. The RRB (Railway Recruitment Board) is conducting the RRB Group D exam to recruit various posts of Track Maintainer, Helper/Assistant in various technical departments like Electrical, Mechanical, S&T, etc. The selection process for these posts includes 4 phases- Computer Based Test Physical Efficiency Test, Document Verification, and Medical Test. Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now! A. 100% B. 75% C. 50% D. 20% Solution(By Examveda Team)$$\eqalign{ & {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr & \,\,\,\,\,\,\,\,\,{\text{1}}\,\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,\,\,\,{\text{4}} \cr & \Rightarrow 4 = 1{\left( {1 + \frac{r}{{100}}} \right)^2} \cr & \Rightarrow 4 = {\left( {1 + \frac{r}{{100}}} \right)^2} \cr & \Rightarrow r = 100\% \cr & \cr & {\text{Alternate}} \cr & {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr & \,\,\,\,\,\,\,\,\,\root 2 \of 1 \,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\root 2 \of 4 \cr & \,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,2 \cr & \Rightarrow {\text{Rate of interest}} \cr & {\text{ = }}\frac{{\left( {2 - 1} \right)}}{1} \times 100 = 100\% \cr} $$ At what rate a sum of money will become four times of itself in 2 years if the interest compounded half yearly?1 Answer. ∴ Required Rate is 82.84% per annum.
At what rate will a sum of money doubles itself in 4 years?∴ The rate of interest is 25%
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How long would it take for a sum to double itself if interest is 4% compounded quarterly?Additionally, the Rule of 72 can be applied across all kinds of durations provided the rate of return is compounded annually. If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal.
What rate percent per annum of compound interest will a sum of money become four times of itself in two years?∴ Rate %=41.42% half yearly and 82.84% p.a. Q. A sum amounts to Rs. 756.25 at 10% per annum in 2 years, compounded annually.
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At what rate would a sum of money becomes 4 times itself if invested for 2 years compounded annually?
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