Assignment 2
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This document contains the questions for Math2701 Assignment 2. It includes 5 questions about calculating present values and payments for various types of annuities with different terms and conditions. Students are asked to solve for values like the payment amount on a revised quarterly annuity, the present value of specific annuities, and the interest rate given equal present values for two perpetuities. The assignment is due on November 19th at the math office by 3:30 pm.
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This document provides an overview of key concepts in bond valuation, equity valuation, and financial mathematics. It defines geometric sequences and series, and explains how to calculate the present value of perpetuities, annuities, growing perpetuities, and delayed perpetuities. It also provides examples of calculating present values for specific financial scenarios.annuity 2.pptx for commerce stream........
annuity 2.pptx for commerce stream........KulsumPaleja1
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An annuity is a series of equal payments made at equal intervals, with key components including periodic payments, payment intervals, and terms. Types of annuities include certain, contingent, ordinary, deferred, and perpetual annuities, each defined by specific payment structures and time frames. Key formulas for calculating future and present values of annuities, as well as for sinking funds, are also presented.Ordinary annuity and annuity due
Ordinary annuity and annuity dueNadeem Uddin
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- An annuity is a series of payments made at regular intervals, typically to provide income for retirement. It can be ordinary (payments made at the end of each period) or due (payments made at the beginning of each period).
- The amount (sum) of an annuity is the total value of all payments over the term. Formulas are provided to calculate the amount based on the payment amount, interest rate, number of periods.
- The present value is the current worth of a future sum or series of sums. Formulas are also provided to calculate the present value of ordinary and due annuities.
- Several examples are provided to demonstrate calculating amounts and present values of ordinary and due annuTime Value Of Money-B.V.Raghunandan
Time Value Of Money-B.V.RaghunandanSVS College
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Time value of money refers to interest or discount rates that account for the timing of money. There are four types of lending/investment calculations: (1) compound interest on a single cash flow, (2) perpetuity, (3) future value of an annuity, and (4) present value of an annuity. The document provides formulas and examples for calculating values under these four types, such as calculating the future value of bonds given the principal, interest rate, and time period. It also discusses factors that determine interest rates and the differences between perpetuity due and perpetuity immediate.Time Value Of Money-B.V.Raghunandan
Time Value Of Money-B.V.RaghunandanSVS College
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Time value of money refers to interest and discount rates that account for the timing of money. There are four types of lending/investment calculations: (1) compound interest on a single cash flow, (2) perpetuity, (3) future value of an annuity, and (4) present value of an annuity. The document provides examples and problems for calculating values under these four types using common time value of money formulas.CFA LEVEL 1- Time Value of Money_compressed (1).pdf
CFA LEVEL 1- Time Value of Money_compressed (1).pdfAlison Tutors
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The document outlines concepts related to the time value of money, including questions and explanations about nominal risk-free rates, risk premiums, ordinary and annuity due calculations, and present value assessments. It covers various financial scenarios, including investments, bank interest rates, and future cash flows, providing formulas and solutions for each case. Overall, it serves as a guide for understanding key principles in finance related to annuities and investment valuations.Lesson 9 deferred annuity
Lesson 9 deferred annuityMLG College of Learning, Inc
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This document defines and provides examples of deferred annuities. A deferred annuity is an annuity where payments do not begin for a period of time. The period of deferral is the time between purchasing the annuity and when payments start. The document provides a time diagram and formulas for calculating the present value of a deferred annuity given the interest rate, payment amount, number of payments, and period of deferral. It includes examples of calculating the present value of deferred annuities for different scenarios.anuity
anuityjohn73067
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This document discusses ordinary general annuities, where the interest conversion period and payment period are different lengths. It provides learning objectives about computing future value, present value, payments, number of periods, and interest rates for ordinary general annuities. It also gives examples of interest conversion periods being longer, shorter, or fractional compared to the payment period. Several practice problems are provided at the end to calculate future values, present values, payments, number of periods, and interest rates for various annuity scenarios.Mathematical Derivation of Annuity Interest Rate and its Application
Mathematical Derivation of Annuity Interest Rate and its ApplicationWaqas Tariq
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The paper presents a mathematical derivation of annuity interest rates and outlines a new computational algorithm that improves efficiency by approximately 99.9% compared to traditional tabulated methods. It discusses various financial applications, including ordinary annuities and their present values, along with methods for calculating interest rates through simplifications. The study highlights the significance of precise calculations in investment scenarios where both individuals and businesses deal with annuities.Ad
Assignment 2
- 1. Math2701 Assignment 2 DUE MONDAY NOVEMBER 19TH AT THE MATH OFFICE BY 3:30 PM QUESTION 1 An annuity certain with payments of 贈150 at the end of each quarter is to be replaced by an annuity with the same term and present value, but with payments at the beginning of each month instead. Calculate the revised payments, assuming an annual force of interest of 10%. QUESTION 2 Joe can purchase one of two annuities: Annuity 1: A 10-year decreasing annuity-immediate, with annual payments of 10, 9, 8, . . . , 1 . Annuity 2: A perpetuity-immediate with annual payments. The perpetuity pays 1 in year 1, 2 in year 2, 3 in year 3, . . . , and 11 in year 11 . After year 11, the payments remain constant at 11. At an annual effective interest rate of i, the present value of Annuity 2 is twice the present value of Annuity 1. Calculate the value of Annuity 1. QUESTION 3 The present value of a 25-year annuity-immediate with a first payment of 2500 and decreasing by 100 each year thereafter is X. Assuming an annual effective interest rate of 10%, calculate X. QUESTION 4 A member of a pensions savings scheme invests 1,200 per annum in advance, for 20 years from his 25th birthday. From the age of 45, the member increases his investment to 2,400 per annum. At each birthday thereafter the annual rate of investment is further increased by 100 per annum. The investments continue to be made annually in advance for 20 years until the individuals 65th birthday. Calculate the accumulation of the investment at the age of 65 using a rate of interest of 6% per annum effective. QUESTION 5 Sandy purchases a perpetuity-immediate that makes annual payments. The first payment is 100, and each payment thereafter increases by 10. Danny purchases a perpetuity-due which makes annual payments of 180. Using the same annual effective interest rate, i > 0, the present value of both perpetuities are equal. Calculate i. (4 marks)