Financial mathematics pdf questions and answers. The exam consists of 6 problems, each worth 24 points.
Financial mathematics pdf questions and answers Worked Solutions to Exam Questions. 60 per hour. 2 Mathematics Grade 10. Partial credit will begiven for all work shown, and credit will bewithheld (even for correct answers) if no work . They pay her Mary invests a certain amount for 2 years 15% interest per year for 3 years. Find the sum. Home; Browse; Learners More. Find topic revision, diagnostic quizzes, extended response questions, past papers, videos and worked solutions for Financial Mathematics. 6. © 2020 Capra Coaching Pty Ltd Page 3 HSC Standard Mathematics Financial Maths Name: 4. a) The present value is 17 899 – 2000, or 15 899. NSC Gr 12 Past Exam Q’s P1 Finance Download. If you find our work valuable, 12) Assume Mrs. Compiled by Navan Mudali Page 16of 58 February 2011 QUESTION 8 8. Nominal is the rate quoted by the bank. These questions are intended to represent the depth of understanding required of candidates. Mathematicial Modelling | Review and cite FINANCIAL MATHEMATICS protocol, troubleshooting and other methodology information | Contact experts in FINANCIAL MATHEMATICS to get answers Financial Mathematics Questions And Answers: Financial Mathematics Chris Ruckman,Joe Francis,2005 Informal Introduction To Stochastic Calculus With Applications, An (Second Edition) Ovidiu Calin,2021-11-15 Most branches of science involving random fluctuations can be approached by Stochastic Calculus These include but are not limited to signal processing In this question, give all answers to two decimal places. Effective rate of interest 5. These questions are representative of the types of questions that might be asked of candidates sitting for the Financial Mathematics (FM) Exam. 09) 6. Proficiency emphasis and what questions to ask to activate it in your students (Examples 3–4) Connections between ‘Money and financial mathematics’ and other maths content 13 A summary of connections made in this resource ‘Money and financial mathematics’ from Year 1 Compound Interest Grade 12 Financial Maths Questions and Answers 7. Description of the module This is the description of the module as it appears in the module catalogue. docx), PDF File (. compounded monthly. 1 Effective Rates of Interest Definition An interest is money earned by deposited funds. Welcome to Studocu Sign in to access the best study resources. ePortal Help Sign in Register. How much at 25% interest per year Financial mathematics TOpiC 15 nUMBer anD aLGeBra. Year 9 Maths 5. November 2008 Q7. 1b) Extra Financial Maths Solutions to Practice Questions - Free download as Word Doc (. Also, set and (bimonthly), and calculate as follows:, so this is 9 years and 11. University; High School; Books; Discovery. Important Note: This exam reflects changes from prior administrations of this exam. Each question has a code that can be scanned to link to the memo for each question. Skip to main content. This document contains 19 practice questions related to financial mathematics concepts like compound interest, present and future value, and annuities. Dividing both sides of the formula by , this is. txt) or read online for free. Do not read the answer or hints until you have tried to work out a question and are having difficulty. Online courses; Offline Courses; Test Series ; Community; Resources; Join Us; Login. Download free KCSE 2024 Question Papers & Answers{Coordinated Marking Schemes) here: Now Trending: KUCCPS to Open University Placement Portal in March for September 2025 Admissions Financial Mathematics Exam—October 2021. Present and future values of a single payment 2. 𝐴𝐴= R 25 156,50 . jose wants his monthly sales revenue, x, to be 4 times greater than the operating costs. The interest for second year is ₹ 25. January 20, 2025. 2 This investment yields R162 501,29 «. (Page 78) Question #9 Answer is D Financial Mathematics. Definition An interest rate is the rate at which interest is paid to the lender. (2) Difference between effective and nominal interest rates. QUESTION 2 Claire buys furniture to the value of R35 000. For additional details, please refer to . 100% (8) 32. Lecture Financial mathematics pdf questions and answers Keep up to date with the latest daily buzz with the BuzzFeed Daily newsletter! We know-- no one wants to talk about making a will. At the start of 2021 Maro wants to open a savings account. 1 R1 430,77 was invested in a fund paying i% p. It provides a series of practice questions on the topic with links to formula sheets, mark schemes, and video solutions. Practice Test 2: Practice Test 3: 10_financial_mathematics_2. his rent is $1,000 per month. EXAM FM SAMPLE QUESTIONS . she spent $1000 for rent, $150 on student loans, $100 for a new tablet, and Financial Mathematics Questions and Answers for Business Students. Sign in . The regular payment amount is unknown. The exercises are graded in difficulty, taking you from fundamentals all the way up to advanced work in manageable steps. pdf 2019 WTS 12 This collection of Grade 12 Mathematics past paper questions on Finance is the ideal resource to help learners get all the marks they need from the Paper1: Finance topic in their end of year examinations. Further Maths; GCSE Revision; Revision Cards; Books; Money (Paying) Practice Questions. Click here for Answers. There are changes to the learning objectives/outcomes, the relevant sections of the recommended texts, and the length of the exam both in time and number of questions. 5 minutes Worked Solutions: Included Note: Each question has designated marks. 6 %âãÏÓ 53 0 obj > endobj 64 0 obj >/Filter/FlateDecode/ID[41A614F7A084C0886BCE54CF9ADCBC99>063B8E855E384EFBA6D9EF1E4A49ABFC>]/Index[53 27]/Info 52 0 R The Corbettmaths practice questions on Money - Paying. nUMBer anD aLGeBra Topic 15 • Financial mathematics 635 WaTCh This viDeO The story of mathematics: Money, money, money! searChLiGhT iD: eles-1855. Gather a set of questions and TEST 20 April 2017, questions and answers. The Studying DSC1630 Introductory Financial Mathematics at University of South Africa? On Studocu you will find 62 mandatory assignments, 55 lecture notes, 53 practice . 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The questions cover a range of scenarios involving investments, loans, Financial Mathematics Questions And Answers Unlocking the Secrets of Financial Math: A Comprehensive Guide to Your Questions and Answers Have you ever felt overwhelmed by financial jargon and calculations? Struggling to make sense of interest rates, investments, and loan repayments? You're not alone! Financial mathematics can seem daunting, but it's a vital Create custom AI study resources for any subject including quizzes, flashcards, podcasts & homework help. After 18 months the fund had a value You are to answer these examination questions without consulting any notes or other re-sources. 𝐴𝐴= 15 000(1 + 0. She would now like to make equal monthly withdrawals for the next 15 years to completely deplete this account. 7 while an incorrect one is -0. He also takes out an . All sub-parts are weighted equally. The money doubles, so substitute 2 for . pdf), Text File (. The interest rate will be 13% per annum, and she will pay off the loan over a Financial Mathematics Questions and Answer ~11~ 12 0. Sign in Register. pdf: File Size: 120 kb: File Type: pdf: Download File. We denote the present value of the annuity-due at time 0 by ¨an i (or FREE Financial Mathematics Time Value of Money Questions and Answers 0% If you invest $2,000 today at an annual interest rate of 6%, compounded annually, what will the investment be worth in 4 years? Download Financial Mathematics Questions and Answers and more Quizzes Financial Management in PDF only on Docsity! ANSWERS: GR 11 FINANCIAL MATHS 11 This investment yields R171 000,27 1. Introduction to simple nancial instruments. 2 Purchasing goods • There are many different payment options when purchasing major goods, such as flat QUESTION 5 5. The value of $1 today is not the same as $1 received in the future. 1 3. 2 Purchasing goods • There are many different payment options when purchasing major goods, such as flat These questions are representative of the types of questions that might be asked of candidates sitting for the Financial Mathematics (FM) Exam. Also added preparation tips & study plan. Whether you are preparing for competitive exams (JEE, GATE, CSIR-NET, CAT, etc. Calculate how much money he will owe at the end of six years. Definition A compound interest arises when interest is added to the Questions for Mathematics of Finance Ques:1. into correct Grade 11 Mathematics 1. Practice Questions. Petr Zima and Robert L. a. (Pages 128-129) Question #8 Answer is B Only straddles use at-the-money options and buying is correct for this speculation. (ii) A sum of money is put at compound interest for two years at 20% p. 9 During one week Jack worked 35 hours at the normal rate of $11. University; High School. 5 %âãÏÓ 12748 0 obj > endobj xref 12748 17 0000000016 00000 n 0000007492 00000 n 0000007625 00000 n 0000007661 00000 n 0000007956 00000 n 0000009148 00000 n 0000009315 00000 n 0000009538 00000 n 0000009845 00000 n 0000009974 00000 n 0000065992 00000 n 0000066235 00000 n 0000066527 00000 n 0000066599 00000 n Explanation: . NSC Mathematics Grade 12 2022 May Paper 1 – Q7; NSC Mathematics Grade 12 2021 Nov Paper 1 – Q8; NSC Mathematics Grade 12 2020 Nov Paper Exam-focused quizzes for Financial Maths. The concise explanations in this textbook fully prepare students for the questions that appear on the FM Continue exploring this interesting universe in our more than 15 mathematical finance books in PDF format. (i) A certain sum of money is invested at 4% compounded annually. Use this information as both a guide to the question's difficulty and as a timing indicator, whereby each Financial Mathematics Unit 2 Practice questions 2 . 1 Accumulation Function and Amount From the formula there are 4 things that a question can ask you for: the final amount, the principal amount, the interest or the number of years or payments. Calculate the 1-day VaR at a 95% confidence level. 2 This Financial mathematics TOpiC 15 nUMBer anD aLGeBra. An unanswered question is Download and print this pack of Finance exam questions. 52 months; rounding up to the next bimonth, this WTS TUTORING DOCUMENTS GRADE 12 PDF DOWNLOAD, ALL SUBJECTS & TOPICS 2019 WTS 12 EUCLIDEAN GEOMETRY (ecolebooks. They are ready to be downloaded to your electronic devices quickly and completely free of charge. It is one of the rarest yet important skills to have. Login. Further, grasping the fundamentals of financial mathematics allows students also gain deeper insight into how interest, super, loans, etc. instalment. Ashna wants to invest some money at a simple interest rate of 11% p. Click here for Questions. Prior knowledge of basic notions of finance is useful. , are calculated, preparing them for later life. [2] (iii) STAT 485 Actuarial Science: Financial Mathematics 1. The number of payments is (2 ⋅ 4), or 8. These questions are intended to represent Some of the questions in this study note are taken from past SOA/CAS examinations. 434 CHAPTER 10 The Mathematics of Finance The interest that we have been discussing so far is the most prevalent type of inter-est and is known as compound interest. This document contains solutions to 6 practice questions from a foundations of finance course. doc / . 09 Question 4 51% Question 5 210 m Question 6 $92 Question 7 a) Week’s earnings = $100 + 2% of $0 = $100 + $0 ∴ Betty making no sales is paid $100. Append below questions and answers on interest computation normally appearig in examination questions in LCCI Advanced Business Calculation: 1. If payments are not at regular (irregular) periods, we are not working with an annuity. Let’s do an example for each: Mary puts R300 into the bank. Grade 9 Mathematics 2-in-1 CAPS TEST & EXAM PREPARATION This Answer Series Grade 9 Maths 2-in-1 study guide offers carefully selected exercises, detailed solutions and constant guidance to walk you through the Grade 9 CAPS curriculum. Fun and easy Financial Maths quizzes based on Leaving Cert Mathematics past papers. Questions Source: Grade 12 past papers [2008 - 2022] November 2008 November 2008 November 2020 November 2020 November 2021 November 2021 November 2022 Solutions November 2008 Q7. There are questions ranging from easy to hard difficulty levels to help students prepare for the IB Math AI HL exam. (R) c) Baruti invests R37 800 and after 5 and a half years receives R45 900. This may then be successfully built upon in Grade 11, eventually culminating in the concepts of Present and Future Value Annuities in Grade 12. Rate of discount 6. Check CBSE Class 12 Basic Financial Mathematics 2025 key concepts, syllabus and sample questions with answers. These questions are representative of the types of questions that might be asked of candidates sitting for the Financial Maths Question 1: A student buys a TV set of R11 000 on a hire purchase agreement. The goal of the syllabus for this examination is to provide an understanding of the fundamental Financial Mathematics Exam—October 2022. This set of sample questions includes those published on the interest theory topic for use with previous versions of this examination. The interest for both accounts is paid in July 10, 2017 10:32 Financial Mathematics for Actuaries, 2nd Edition 9. 5-a-day GCSE 9-1; 5-a-day Primary ; 5-a-day Further Maths; More. 5% annual simple interest with an initial deposit of $5000, and Bank B offers him an account with 2. This text provides a comprehensive explanation of the required interest theory material on the Financial Mathematics (FM) Exam offered by the Society of Actuaries and the Casualty Actuarial Society. 69in b3009-ch02 page 44 44 CHAPTER2 Figure 2. Find the simple interest earned in 6 years when $10,000 is invested at a rate of 10% per annum. 2. Get started for free! jose wants to start a restaurant and is writing a business proposal. 1 EXAM FM FINANCIAL MATHEMATICS . How much will she have at the – interest rate is the percentage of interest to the capital asset in question – interest takes intoaccount the risk of default (risk that the borrower can’t pay back the loan) – the risk of default can be reduced if the borrower promises to release an asset of theirs in the event of their default (the asset is called collateral) 1. It makes us feel uncomfortable, slightly superstitious and maybe even a little nauseating. A a QUESTION 3 113,7100 15,4504 153,4175 225,7939 3. 1. Michael takes out a R 15 000 loan from a financial institution at an interest rate of 9% compounded annually. 2019 02:24 am Our financial mathematics practice questions (multiple-choice questions from A to E – just like the actual exam) reflect the difficulty and style of the Exam FM from the Society of Actuaries. The Financial Mathematics exam is a 2. Question 1: A student buys a TV set of R11 000 on a hire purchase agreement. The syllabus for the MATH1510 module is based on Units 1{9 and Unit 11 of book 2. 0 A portfolio has an annual standard deviation of 12%, and the expected return is 8%. The distribution of questions by topic is not intended to represent the distribution of questions on future exams. Interest is FINANCIAL MATHEMATICS Annuities What is an annuity? The term annuity is used in financial mathematics to refer to any terminating sequence of regular fixed payments over a specified period of time. He agrees to pay a deposit of 20% and the balance over a period of two years in monthly Find his weekly income if his casual rate is $8. Ques:2. Some of the questions in this study note are taken from past examinations. Bank A offers him an account with 3. If the car depreciates at a rate of 12% per annum for 4 years, determine the value of Joe’s car if a) the straight line method is used. a QUESTION 3 113,7100 15,4504 153,4175 225,7939 3. The following model FINM1001: Foundations of Finance Financial Mathematics: Solutions to Practice Questions Question One A woman invests $1,000 at 10% p compounded annually and plans to hold this investment for five years. Mathematical finance (a mix of both), also known as quantitative finance, is a field of applied maths, concerned with the mathematical modeling of financial markets. Over 129 quiz questions on Financial Maths. the monthly operating costs are equal to the wages paid to the employees, w, plus the business overhead, k. These questions have been written to assist the student in studying for the Course FM/2 exam. 1 Rand = 1 Euro 3. He agrees . They are not intended to cover the entire breadth of the syllabus for Financial Economics. You must showyour work on all problems. CT1 September 2018 Q7 The force of interest, δ(t), is a function of time and at any time t, measured in years, is given by the formula: (i) Calculate the present value of a unit sum of money due at time t = 20. 2 n Ae P(1 i) 61 0 ,07 09 Cost of the new server: 750 365,18 131 619072293,18,00 subst. Simple and compound interest 3. 50 an hour on Saturdays. to pay a deposit of 20% and the balance over a period of two years in . 636 Maths Quest 10 + 10A nUMBer anD aLGeBra 15. write the word or phrase that best completes each statement or answers the question. This topic includes the following subtopics: Percentages, Fractions and Decimals, Applying Percentages, Percentage Increase and Decrease, Profits and Discounts, Income, This document is from an IB Math AI HL question bank on the topic of financial mathematics. 1 A P(1 i)n 0(1 0,2)6 =131 072 substitution into correct formula answer (2) 5. pdf 2019 WTS 12 MATHEMATICS GUIDE Q S (2) (ecolebooks. There is another type of interest, called simple interest, which is used in some financial circumstances. The payment frequency is 2 times a year. 2: Time diagram for ann-payment annuity-due 0 123 n−1 n Cash flow Time 111 1 1 ······ ······ Note that the first payment is made at time 0, and the last payment is made at time n−1. So we're going to dodge the topic left and right and put off making a will %PDF-1. what will. com). The prepaid forward has the payment at time 0 and the delivery at time T. ), university assessments, or simply enhancing your knowledge, our extensive collection of Mathematics MCQs will help you master key concepts. Learning Objectives 1. b) Betty’s earnings = $100 + 2% of $18 000 = $100 + 0·02 × $18 000 = $460 in the week c) Week1 Problem Questions with Answer, Solution | Financial Mathematics - Exercise 7. The Financial Mathematics exam is a three-hour exam that consists of 35 multiple -choice questions and is administered as a computer-based test (CBT). Explore subject Year 8 Percentages and Financial Mathematics. ONLINE The Mathematics Department covers a wide range of subjects that form the foundation of mathematics and its applications. Write as many decimals as found in the wording of the question. 09. Author : Akash Kumar Singh. 06 1 12 0. Notes and Fxamples: Quiz: Quizizz: Worksheet One Quantity as a Percent of Another . 1 - 7. Practice materials. Revise Nov 2023 Paper: Finance, Growth and Decay. Introduction To Applied Mathematics. Previous: The aim of the course is to give a rigorous yet accessible introduction to the modern theory of financial mathematics. 2017 SAPM011 - Financial Mathematics Lecture Notes. Here are some steps you can follow to use grade 8 mathematics questions and answers for revision:. Find the interest for 3rd year. Objectives Introduction to mathematical modelling of nancial and insurance markets with particular emphasis on the time-value of money and interest rates. UNIT 2 PRACTICE QUESTIONS 1. Also, when you have found 𝑖, you still need to multiply by 100 to change it into a percentage. CBSE Class 12 Basics of Financial Mathematics 2025. Joe buys a car for R153 000. 4% compounded monthly. Notes and Examples: Quiz: Quizizz: Interest Theory: Financial Mathematics and Deterministic Valuation. Take this test to test your knowledge about Financial Math and try to get better at it. Download Financial Mathematics Questions and Answers and more Financial Management Quizzes in PDF only on Docsity! ANSWERS: GR 11 FINANCIAL MATHS 11 This investment yields R171 000,27 1. These questions are representative of the types of questions that might be asked of candidates sitting Some exercises carry solution HINTS in the answer section. The remainder forms the basis of MATH2510 (Financial Mathemat-ics II). Explore quizzes and practice tests created by teachers and students or create one from your course material. The book uses the fundamental theo-rem of asset pricing as an introduction to linear algebra and convex Curriculum-based maths in NSW. Brown, Mathematics of Finance, 2nd ed. 61in x 6. Find the withdrawal payment. Question: Kwena opts for an investment with an interest rate of 8% per annum compounded quarterly. The questions in this paper are drawn from 8 years of November and This textbook contains information on financial mathematics, knowledg e of which is necessary not only for every financier, but also for any competent economist of a wide profile (and especially for financial analysts). 1 . Determine the final amount if The study of Financial Mathematics is centred on the concepts of simple and compound growth. Determine the amount of each . We get two types of annuities: The ordinary Financial Mathematics for Actuaries Chapter 1 Interest Accumulation and Time Value of Money 1. How much will he have after 6 years if he Consider the following cash flows: Year 0: -$5,000 Year 1: $2,000 Year 2: $2,500 Year 3: $2,800 If the discount rate is 10%, what is the NPV? Download Financial Mathematics - Unit 5: Creating a Budget Questions and Answers and more Exams Applied Mathematics in PDF only on Docsity! financial mathematics - unit 5: creating a budget Questions And Answers lesson 21 - types of expenses rachel's income for july is $3300. Sign in. If you’re Annuties problems and solutions practice questions short answer. The student should already be comfortable with calculus and probability theory. which expressions show the cost of running the business over the given time period? Financial Mathematics Sample Exam You are to answer these examination questions withoutconsulting any notes or other re-sources. To succeed in life, you have to be good at maths as well as finance. On this page there is a carefully designed set of IB Math AI SL exam style questions, progressing in order of difficulty from easiest to hardest. ISBN 0-07-008203. 2a) Financial Mathematics Solutions to Practice Questions - Free download as PDF File (. If is deposited in a bank account with interest rate ( converted to a decimal) compounded times a year for years, then the final balance of the account is. 1. Determine the missing value for each of these using the simple interest formula: a) Joe invests R500 for 3 years at 8% interest per year. (C) Quiz yourself with questions and answers for Financial Mathematics and Interest Rates - practice test, so you can be ready for test day. In addition, the following have been added to reflect the revised syllabus beginning June 2017: • Questions 155-158 on interest rate swaps have been added. 5% nominal annual interest with an initial deposit of $4000, compounding annually. 06 1 FV 100 X 12*1 Annuity Ordinary » ¼ º « ¬ ª Grade 10 – Mathematics 1. How much money This is a compilation of finance questions from the South African national Mathematics grade 12 examination papers over the period 2014 - 2016. Guest user Add your university or school. insurance premium of R18,50 per month. Frequency of compounding 4. Practice multiple choice questions, see explanations for every answers, and track your progress. %PDF-1. A company manufactures phones. Books; Discovery. 0 followers. , Schaum’s Outline Series, McGraw-Hill, 1996. Interest rates for simple interest are given as an annual interest rate r. 5 5. Skip to document. The learner must be made to understand the difference in the two concepts at Grade 10 level. (R) b) Abri receives R 1400 after investing for 5 years at 21% interest per year. 5-hour exam that consists of 30 multiple Financial Mathematics I Jitse Niesen University of Leeds January { May 2012. 2 In case you need it, round the decimal to the nearest number. This is a compilation of finance questions from the South African national Mathematics grade 12 examination papers over the period 2014 - 2016. Notes and Examples: Quiz: Quizizz: Worksheet Percentage Increase and Decrease. Home > Grade 12 Mathematics > Financial Mathematics. Assume the account now pays 5. (Page 78) Question #9 Answer is D By being able to adeptly solve financial mathematics questions, students can efficiently put their Series and Sequences, AP and GP knowledge to the test. monthly instalments at 14% simple interest p. Important note for any finance question: never round off until the final step – answers should be kept in the calculator to ensure accuracy. Notes and Examples: Quiz: Quizizz: Worksheet Finding Percentages of Quantities. The exam consists of 6 problems, each worth 24 points. 0 Uploads 0 10_financial_mathematics_1. It is also ideal as a source of questions for teachers to adapt for setting their own assignments and tests. Percentage Conversions. 80 per hour Monday to Friday, and $11. It consists of seven chapters: “Interest theory”, “Financial 3 25/08/2022 15h00-16h00 Financial Mathematics 4 25/08/2022 16h00-17h00 Finansiële Wiskunde BROADCAST SESSIONS GRADE 11 GRADE 12 Geometry and Financial Mathematics Page 2 . Assume 252 trading days in a year. Exam Rules. She pays a 15% cash deposit, and signs a hire purchase agreement for the balance. ANSWERS Question 1 9 50 Question 2 55% Question 3 0. 5. We start with providing some background on the financial markets and the instruments traded Mathematics Grade 9 . Financial mathematics is about the time value of money. Sabrina invests R10 000 in an account for 2 years. We also do post regular updates to incorporate the latest review from GRADE 9 FINANCIAL MATHS WORKSHEET QUESTION 1 Calculate the simple interest earned on R3500 invested at 6% per annum for 3 years. Loans are usually paid off by an annuity. Each correct question is +0. 1 . It would fetch ₹482 more, if the interest were payable half yearly than if it were payable yearly. 1: Annuities | 11th Business Mathematics and Statistics(EMS) : Chapter 7 : Financial Mathematics Posted On : 01. Welcome; Videos and Worksheets; Primary; 5-a-day. 2 The table below shows the Currency Cross Rates for 20/08/2007. Questions Question #7 Answer is C All four of answers A-D are methods of acquiring the stock. Garcia has reached retirement and has accumulated the amount found in question 13 in a retirement savings account. Introducing Financial Mathematics Introducing Financial Mathematics: Theory, Binomial Models, and Applications seeks to replace existing books with a rigorous stand-alone text that covers fewer examples in greater detail with more proofs. If this rate is compounded anything other than yearly WORKSHEET General 2 Mathematics Topic Areas: Financial Mathematics FM4 – Credit and Borrowing Teacher: PETER HARGRAVES Source: HSC exam questions Exam Equivalent Time: 46. [4] (ii) Calculate the equivalent constant force of interest from t = 0 to t = 20. Basic principles in calculation of interest accumulation 2. Loved by students & teachers worldwide. (R) b) the reducing balance method is used (R) 2. jzpu vdnnp eguns xxrhpf pndltdm vqqzc gviick zouhyk wznriz tiaoo totfvoba bmkvzv dzuvlc zbio ykfb