# How To Calculate A Pension

Size: px
Start display at page:

Transcription

1 Interests on Transactions Chapter PV & FV of Annuities

2 PV & FV of Annuities An annuity is a series of equal regular payment amounts made for a fixed number of periods 2

3 Problem An engineer deposits P1,000 in a savings account at the end of each year for 5 years. How much money can he withdraw at the end of 5 years if the bank pays interest at the rate of 6% p.a., compounded annually?

4 An engineer deposits P1,000 in a savings account at the end of each year for 5 years. How much money can he withdraw at the end of 5 years if the bank pays interest at the rate of 6% p.a. compounded annually? FV = PV ( 1 + i) ⁿ FV = 1000(1.06)⁴ (1.06)³ (1.06)² (1.06) = P5, FV

5 An engineer deposits P1,000 in a savings account at the end of each year for 5 years. How much money can he withdraw at the end of 5 years if the bank pays interest at the rate of 6% p.a. compounded annually? FV = FV( rate, nper, pmt, pv, type) FV = FV (.06,4,0,-1000,0) + FV (.06,3,0,-1000,0) + FV (.06,2,0,-1000,0) + FV(.06,1,0,-1000,0) + FV(.06,0,0,-1000,0) = P5, FV

6 An engineer deposits P1,000 in a savings account at the beginning of each year for 5 years. How much money can he withdraw at the end of 5 years if the bank pays interest at the rate of 6% p.a., compounded annually? FV = PV ( 1 + i) ⁿ FV = 1000(1.06)⁵ (1.06)⁴ (1.06)³ (1.06)² (1.06) = P5, (1.06) = P5, FV

7 An engineer deposits P1,000 in a savings account at the beginning of each year for 5 years. How much money can he withdraw at the end of 5 years if the bank pays interest at the rate of 6% p.a., compounded annually? FV = FV (rate, nper, pmt, pv, type) FV=FV(.06,5,0,-1000,0) + FV(.06,4,0,-1000,0) + FV(.06,3,0,-1000,0) + FV(.06,2,0,-1000,0) + FV(.06,1,0,-1000,0) = P5, FV

8 FV = PV ( 1 + i ) ⁿ FV = 1000 (1.06)⁵ (1.06)⁴ (1.06)³ (1.06)² +1000(1.06) FV = Pmt (1 + i)ⁿ + Pmt ( 1+ i)ⁿ ᶦ + Pmt (1 + i)ⁿ ² + Pmt(1 + i)ⁿ ³ + Pmt (1 + i)ⁿ ⁴ Pmt (1 + i)ⁿ ⁿ 1000 = Pmt 0.06 = i Geometric series: a + ax + ax² + + ax³ ax ⁿ ¹ Summation = Sn = a (1-xⁿ) (1-x) x = ratio of successive terms = [Pmt (1+i)ⁿ ᶦ] /[Pmt (1+i)ⁿ ᶦ] = 1 / (1+i) a = first term = Pmt(1+i)ⁿ FV = {Pmt(1+i)ⁿ} {1-[1/(1+i)]ⁿ} / {1 [1/(1+i)]} = Pmt (1+i)ⁿ [(1+i)ⁿ-1)/(1+i)ⁿ] /[(1+ i 1) / (1+i)] FV = {Pmt (1+i) [(1+i)ⁿ-1)]} / i annuity due formula

9 Basic Formula to Use B Loan Balance after n payments = FV Compounding FV annuity (5) B = PV (1 + i ) ⁿ - Pmt[ (1 + i)ⁿ -1] i (1) FV compounding = PV ( 1 + i ) ⁿ single transaction (2) PVdiscounting = FV ( 1+ i ) ⁿ single transaction (3) FV annuity = Pmt [(1 + i)ⁿ -1] ordinary annuity i (4) PV annuity = Pmt [1 (1 + i ) ⁿ] ordinary annuity i 9

10 Basic Formula to Use B Loan Balance after n payments = FV Compounding FV annuity (5) B = PV (1 + i ) ⁿ - Pmt[ (1 + i)ⁿ -1] i (1) FV compounding = PV ( 1 + i ) ⁿ = FV (rate, nper, 0, pv, 0) (2) PVdiscounting = FV ( 1+ i ) ⁿ = PV (rate, nper, 0, fv, 0) (3) FV annuity = Pmt [(1 + i)ⁿ -1] ordinary annuity i = FV (rate, nper, pmt, pv, 0) (4) PV annuity = Pmt [1 (1 + i ) ⁿ] ordinary annuity i = PV (rate, nper, pmt, fv, 0) 10

11 An engineer deposits P1,000 in a savings account at the end of each year for 5 years. How much money can he withdraw at the end of 5 years if the bank pays interest at the rate of 6% p.a., compounded annually? Method 1: Single transaction FV = PV ( 1 + i ) ⁿ = 1000(1.06)⁴ (1.06)³ (1.06)² (1.06) = P5, Method 2: FV annuity = Pmt [ (1 + i)ⁿ -1] i = [1000] [(1.06)⁵ -1] / [0.06] Method 3: = FV (rate, nper, pmt, pv, type) = FV ( 0.06, 5, -1000, 0, 0 )

12 B. Annuities: A series of equal payments A. Ordinary Annuity: Regular deposits are made at the end of the period. B. Annuities Due: Regular deposits are made at the beginning of the period 12

13 Annuity Due = Ordinary Annuity x (1 + i) [Present value same formula] Future Value of an investment three years after, for a \$3000 annuity at 8%. Ordinary Annuity \$3000 \$3000 \$3000 Year 1 Year 2 Year 3 FV Annuity Due \$3000 \$3000 \$3000 Year 1 Year 2 Year 3 FV 13

14 I. Ordinary Annuity: Future Value Toby Martin invests \$2,000 at the end of each year for 10 years at 11% p.a., compounded annually. What is the final value of Toby s investment at the end of year 10? 1) By Table: Periods = 10 x 1 = 10 ; Rate = 11 % / 1 = 11% Table 13-1 Table Factor = Future Value = \$2,000 X = \$ 33,444 14

15 Toby Martin invests \$2,000 at the end of each year for 10 years at 11% p.a., compounded annually. What is the final value of Toby s investment at the end of year 10? 2) FV = Pmt [(1 + i )ⁿ -1] i = 2000 x {[(1.11¹⁰) -1] / [0.11]} = 2000 x ( )/ (0.11) = \$33,444 3) = FV (rate, nper, pmt, pv, type) Excel = FV( 0.11, 10, -2000, 0, 0) = \$33,444 15

16 II. Annuity Due = Ordinary Annuity x (1 + i) Tony invests \$3000 at the start of each year at 8% p.a., compounded annually. Find its value at the end of three years. Future Value: Ordinary Annuity FV Ordinary= Pmt [ (1+ i )ⁿ - 1] i = 3000 [(1.08)³ -1] / [.08] = \$9, Future Value: Annuity Due FVDUE = \$9, x (1.08) = \$10,

17 Annuity Due By Table 13-1 of textbook: Future Value: Ordinary Annuity n = 3, i = 8%, table factor = FV = 3000 x = \$9, Future Value: Annuity Due Add one period & subtract one payment n = 4, i = 8%, table factor = FV = [3000 x ] 3000 = \$10,

18 Annuity Due Future Value: Ordinary Annuity n = 3, i = 8% Excel: = FV (0.08,3,-3000,0,0) = \$9, Future Value: Annuity Due n = 3, i = 8% Excel: =FV (0.08,3,-3000,0,1) = \$10,

19 # 9 # At the beginning of each 6-month period for 10 years, Merl Agnes invests \$500 at 6% p.a., compounded semi-annually. What would be its cash value at the end of year 10? 1) Formula: FV = 500 [(1.03)²⁰ -1] (1.03) 0.03 = [500 [ / 0.03] (1.03) = \$13, ) = FV ( 0.03, 20, -500, 0, 1) = \$13,

20 Annuities Due: Future Value # At the beginning of each 6-month period for 10 years, Merl Agnes invests \$500 at 6% p.a., compounded semi-annually. What would be its cash value at the end of year 10? Step 1: Calculate the number of periods and the rate per period. Add one extra period. Periods = 10 X 2 = 20, add 1 extra, = 21 ; Rate = 6% / 2= 3 % Step 2: Look up in an Ordinary Annuity Table 13.1 the table factor based on the above computed periods and rate. This is the future value of \$1. Table Factor = Step 3: Multiply payment(deposit) each period by the table factor: \$500 X = \$14, Step 4: Subtract one payment from Step3 to get Future Value of Annuity Due Future Value = \$14, \$500 = \$13,

21 II. Ordinary Annuity: Present value On Joe s graduation from college, his uncle promised him a gift of \$12,000 in cash, or \$900 every quarter for the next 4 years after graduation. If money could be invested at 8% p.a., compounded quarterly, which offer is better for Joe? 1) By Table: Periods = 4 X 4 = 16 Rate = 8% / 4 = 2 % Table 13 2 Factor = PV = \$ 900 X = \$ 12, Annuity is better than \$ 12,000 cash 21

22 PV Ordinary Annuity On Joe s graduation from college, Joe s uncle promised him a gift of \$12,000 in cash, or \$900 every quarter for the next 4 years after graduation. If money could be invested at 8% p.a., compounded quarterly, which offer is better for Joe? 2) Formula: PV = Pmt [1 (1+ i ) ⁿ] i = 900 x [1 (1.02) ⁴*⁴]/ [0.02] = \$12, ) Excel: = PV ( 0.02, 16, 900, 0,0)= -\$12,

23 Sinking Fund annuity where the equal periodic payments are determined Jeff Associates plans to setup a sinking fund to repay \$30,000 at the end of 8 years. Assume an interest rate of 12% p.a., compounded semi-annually. 1) By Table 13-3: n = 8x 2= 16; rate = 12% / 2 = 6% Table 13 3 factor = Sinking Fund = \$ 30,000 X.0390 = \$1,170 23

24 Sinking Fund Jeff Associates plans to setup a sinking fund to repay \$30,000 at the end of 8 years. Assume an interest rate of 12% p.a., compounded semiannually. Formula: Pmt = FV [ i ] [ (1+ i)ⁿ - 1] = * {.06/[(1.06)⁸*² -1]} = \$1, Excel: = PMT(rate, nper, pv, fv, type) Excel: = PMT (0.06, 16, 0, 30000,0) = -\$1,

25 Monthly payment & Payoff amount Mr. Joson buys a car for P1M. A down payment of 20% of the car price is paid in cash, with the balance to be paid in 36 months. The interest rate is 14.25% p.a., compounded monthly. After 24 months of paying, Mr. Joson would like to know his payoff amount. i = 14.25% / 12 = per month PV = P1M P200K = P800,000 n = 36 months First step: Find monthly payment amount

26 Monthly Payment PV = [Pmt/i][ 1 (1 + i ) ⁿ] Pmt = [i PV ]/[1 (1 + i) ⁿ] = [( )(800,000) = P27, [ 1 ( ) ³⁶ ] Using Excel: pmt(rate, nper, pv, fv, type) = pmt ( , 36, , 0, 0) = P27, Second Step: Find the payoff amount

27 Payoff Amount B Loan Balance after n payments = FV Compounding FV annuity B = PV (1 + i ) ⁿ - Pmt[ (1 + i)ⁿ -1] i = 800,000 ( )²⁴ - 27, [ ( )²⁴ - 1] = 1,062, , = P305, Excel: = FV ( rate, nper, pmt, pv, type) Method 1: = FV( , 24, 0, , 0) - FV( , 24, , 0, 0) Method 2: = FV( , 24, , , 0) = P305, amount still to be paid Add Timeline Drawing

28 END

### The Time Value of Money C H A P T E R N I N E

The Time Value of Money C H A P T E R N I N E Figure 9-1 Relationship of present value and future value PPT 9-1 \$1,000 present value \$ 10% interest \$1,464.10 future value 0 1 2 3 4 Number of periods Figure

### Finding the Payment \$20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = \$488.26

Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive \$5,000 per month in retirement.

### Compounding Quarterly, Monthly, and Daily

126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,

### TIME VALUE OF MONEY (TVM)

TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate

### Chapter The Time Value of Money

Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest

### Chapter 3 Mathematics of Finance

Chapter 3 Mathematics of Finance Section 3 Future Value of an Annuity; Sinking Funds Learning Objectives for Section 3.3 Future Value of an Annuity; Sinking Funds The student will be able to compute the

### A = P (1 + r / n) n t

Finance Formulas for College Algebra (LCU - Fall 2013) ---------------------------------------------------------------------------------------------------------------------------------- Formula 1: Amount

### How To Use Excel To Compute Compound Interest

Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout

### Chapter 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest \$1,000 at 6% simple interest for 3 years.

6-1 Chapter 6 Time Value of Money Concepts 6-2 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in

### DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS

Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need \$500 one

### Chapter 4: Time Value of Money

FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. \$100 (1.10)

### Solutions to Time value of money practice problems

Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if \$2,500 is deposited today and the account earns 4% interest,

### Problem Set: Annuities and Perpetuities (Solutions Below)

Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save \$300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years

### TIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!

TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest \$1,000 it becomes \$1,050 \$1,000 return of \$50 return on Factors to consider when assessing Return on

### 1. If you wish to accumulate \$140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?

Chapter 2 - Sample Problems 1. If you wish to accumulate \$140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will \$247,000 grow to be in

### Regular Annuities: Determining Present Value

8.6 Regular Annuities: Determining Present Value GOAL Find the present value when payments or deposits are made at regular intervals. LEARN ABOUT the Math Harry has money in an account that pays 9%/a compounded

### Sample problems from Chapter 10.1

Sample problems from Chapter 10.1 This is the annuities sinking funds formula. This formula is used in most cases for annuities. The payments for this formula are made at the end of a period. Your book

### TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY

TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction In this assignment we will discuss how to calculate the Present Value

### Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows

1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter

### Discounted Cash Flow Valuation

BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?

### 10.3 Future Value and Present Value of an Ordinary General Annuity

360 Chapter 10 Annuities 10.3 Future Value and Present Value of an Ordinary General Annuity 29. In an ordinary general annuity, payments are made at the end of each payment period and the compounding period

### Main TVM functions of a BAII Plus Financial Calculator

Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there

### Lesson 4 Annuities: The Mathematics of Regular Payments

Lesson 4 Annuities: The Mathematics of Regular Payments Introduction An annuity is a sequence of equal, periodic payments where each payment receives compound interest. One example of an annuity is a Christmas

### Bank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is \$75. You will receive \$100 five years later.

ü 4.4 lternative Discounted Cash Flow Decision Rules ü Three Decision Rules (1) Net Present Value (2) Future Value (3) Internal Rate of Return, IRR ü (3) Internal Rate of Return, IRR Internal Rate of Return

### In Section 5.3, we ll modify the worksheet shown above. This will allow us to use Excel to calculate the different amounts in the annuity formula,

Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout

### Chapter 4. The Time Value of Money

Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return

### Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

### Review Page 468 #1,3,5,7,9,10

MAP4C Financial Student Checklist Topic/Goal Task Prerequisite Skills Simple & Compound Interest Video Lesson Part Video Lesson Part Worksheet (pages) Present Value Goal: I will use the present value formula

### FIN 5413: Chapter 03 - Mortgage Loan Foundations: The Time Value of Money Page 1

FIN 5413: Chapter 03 - Mortgage Loan Foundations: The Time Value of Money Page 1 Solutions to Problems - Chapter 3 Mortgage Loan Foundations: The Time Value of Money Problem 3-1 a) Future Value = FV(n,i,PV,PMT)

### Statistical Models for Forecasting and Planning

Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information

### How To Calculate An Annuity

Math 141-copyright Joe Kahlig, 15C Page 1 Section 5.2: Annuities Section 5.3: Amortization and Sinking Funds Definition: An annuity is an instrument that involves fixed payments be made/received at equal

### Discounted Cash Flow Valuation

6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

### International Financial Strategies Time Value of Money

International Financial Strategies 1 Future Value and Compounding Future value = cash value of the investment at some point in the future Investing for single period: FV. Future Value PV. Present Value

### rate nper pmt pv Interest Number of Payment Present Future Rate Periods Amount Value Value 12.00% 1 0 \$100.00 \$112.00

In Excel language, if the initial cash flow is an inflow (positive), then the future value must be an outflow (negative). Therefore you must add a negative sign before the FV (and PV) function. The inputs

### first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest.

ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular

### CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: \$5,000.08 = \$400 So after 10 years you will have: \$400 10 = \$4,000 in interest. The total balance will be

### Mathematics. Rosella Castellano. Rome, University of Tor Vergata

and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings

### Prepared by: Dalia A. Marafi Version 2.0

Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC-200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version

### The Time Value of Money

The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future

### How to calculate present values

How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance

### 13-2. Annuities Due. Chapter 13. MH Ryerson

13-2 Annuities Due Chapter 13 13-3 Learning Objectives After completing this chapter, you will be able to: > Calculate the future value and present value of annuities due. > Calculate the payment size,

### Ordinary Annuities Chapter 10

Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate

### Discounted Cash Flow Valuation

Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

### ANNUITIES. Ordinary Simple Annuities

An annuity is a series of payments or withdrawals. ANNUITIES An Annuity can be either Simple or General Simple Annuities - Compounding periods and payment periods coincide. General Annuities - Compounding

### This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1).

This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/

### 2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?

CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equal-sized

### Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

### Dick Schwanke Finite Math 111 Harford Community College Fall 2015

Using Technology to Assist in Financial Calculations Calculators: TI-83 and HP-12C Software: Microsoft Excel 2007/2010 Session #4 of Finite Mathematics 1 TI-83 / 84 Graphing Calculator Section 5.5 of textbook

### Time Value of Money Problems

Time Value of Money Problems 1. What will a deposit of \$4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. \$8,020.22 b. \$7,959.55 c. \$8,081.55 d. \$8,181.55 2. What will

### Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1

Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation

### Chapter 8. 48 Financial Planning Handbook PDP

Chapter 8 48 Financial Planning Handbook PDP The Financial Planner's Toolkit As a financial planner, you will be doing a lot of mathematical calculations for your clients. Doing these calculations for

### Future Value of an Annuity Sinking Fund. MATH 1003 Calculus and Linear Algebra (Lecture 3)

MATH 1003 Calculus and Linear Algebra (Lecture 3) Future Value of an Annuity Definition An annuity is a sequence of equal periodic payments. We call it an ordinary annuity if the payments are made at the

### The values in the TVM Solver are quantities involved in compound interest and annuities.

Texas Instruments Graphing Calculators have a built in app that may be used to compute quantities involved in compound interest, annuities, and amortization. For the examples below, we ll utilize the screens

### Real estate investment & Appraisal Dr. Ahmed Y. Dashti. Sample Exam Questions

Real estate investment & Appraisal Dr. Ahmed Y. Dashti Sample Exam Questions Problem 3-1 a) Future Value = \$12,000 (FVIF, 9%, 7 years) = \$12,000 (1.82804) = \$21,936 (annual compounding) b) Future Value

### MAT116 Project 2 Chapters 8 & 9

MAT116 Project 2 Chapters 8 & 9 1 8-1: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the

Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

### Chapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)

Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

### Annuities: Present Value

8.5 nnuities: Present Value GOL Determine the present value of an annuity earning compound interest. INVESTIGTE the Math Kew wants to invest some money at 5.5%/a compounded annually. He would like the

### Using the Finance Menu of the TI-83/84/Plus calculators KEY

Using the Finance Menu of the TI-83/84/Plus calculators KEY To get to the FINANCE menu On the TI-83 press 2 nd x -1 On the TI-83, TI-83 Plus, TI-84, or TI-84 Plus press APPS and then select 1:FINANCE The

### 1. Annuity a sequence of payments, each made at equally spaced time intervals.

Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology

### Finance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization

CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need

### Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of

### CHAPTER 9 Time Value Analysis

Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 9-1 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams

Chapter 13 Annuities and Sinking Funds McGraw-Hill/Irwin Copyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved. #13 LU13.1 Annuities and Sinking Funds Learning Unit Objectives Annuities:

### Basic financial arithmetic

2 Basic financial arithmetic Simple interest Compound interest Nominal and effective rates Continuous discounting Conversions and comparisons Exercise Summary File: MFME2_02.xls 13 This chapter deals

### https://assessment.casa.uh.edu/assessment/printtest.htm PRINTABLE VERSION Quiz 4

1 of 6 2/21/2013 8:18 AM PRINTABLE VERSION Quiz 4 Question 1 Luke invested \$130 at 4% simple interest for a period of 7 years. How much will his investment be worth after 7 years? a) \$169.40 b) \$166.40

### The time value of money: Part II

The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods

### Appendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition

C- 1 Time Value of Money C- 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future

### Time Value of Money, Part 5 Present Value aueof An Annuity. Learning Outcomes. Present Value

Time Value of Money, Part 5 Present Value aueof An Annuity Intermediate Accounting II Dr. Chula King 1 Learning Outcomes The concept of present value Present value of an annuity Ordinary annuity versus

### 1.3.2015 г. D. Dimov. Year Cash flow 1 \$3,000 2 \$5,000 3 \$4,000 4 \$3,000 5 \$2,000

D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of

### T12-1 REVIEW EXERCISES CHAPTER 12 SECTION I

T12-1 REVIEW EXERCISES CHAPTER 12 SECTION I Use Table 12-1 to calculate the future value of the following ordinary annuities: Annuity Payment Time Nominal Interest Future Value Payment Frequency Period

### NPV calculation. Academic Resource Center

NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year

### Calculations for Time Value of Money

KEATMX01_p001-008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with

### Lesson 1. Key Financial Concepts INTRODUCTION

Key Financial Concepts INTRODUCTION Welcome to Financial Management! One of the most important components of every business operation is financial decision making. Business decisions at all levels have

### USING THE SHARP EL 738 FINANCIAL CALCULATOR

USING THE SHARP EL 738 FINANCIAL CALCULATOR Basic financial examples with financial calculator steps Prepared by Colin C Smith 2010 Some important things to consider 1. These notes cover basic financial

### hp calculators HP 20b Time value of money basics The time value of money The time value of money application Special settings

The time value of money The time value of money application Special settings Clearing the time value of money registers Begin / End mode Periods per year Cash flow diagrams and sign conventions Practice

### Future Value. Basic TVM Concepts. Chapter 2 Time Value of Money. \$500 cash flow. On a time line for 3 years: \$100. FV 15%, 10 yr.

Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated

### CS-150L Computing for Business Students Future Value of a Retirement Annuity

CS-150L Computing for Business Students Future Value of a Retirement Annuity Instructor: Matthew Barrick e-mail: barrick@cs.unm.edu www.cs.unm.edu/~barrick Office: Farris Engineering Center (FEC) room

### THE VALUE OF MONEY PROBLEM #3: ANNUITY. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction

THE VALUE OF MONEY PROBLEM #3: ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction Earlier, we explained how to calculate the future value of a single sum placed on deposit

### Module 5: Interest concepts of future and present value

Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities

### TVM Functions in EXCEL

TVM Functions in EXCEL Order of Variables = (Rate, Nper, Pmt, Pv, Fv,Type, Guess) Future Value = FV(Rate,Nper,Pmt,PV,Type) Present Value = PV(rate,nper,pmt,fv,type) No. of Periods = NPER(rate, pmt, pv,

### Finance Unit 8. Success Criteria. 1 U n i t 8 11U Date: Name: Tentative TEST date

1 U n i t 8 11U Date: Name: Finance Unit 8 Tentative TEST date Big idea/learning Goals In this unit you will study the applications of linear and exponential relations within financing. You will understand

### Time Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)

Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for

### Chapter F: Finance. Section F.1-F.4

Chapter F: Finance Section F.1-F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given

### Appendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C- 1

C Time Value of Money C- 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C- 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.

### Calculating Loan Payments

IN THIS CHAPTER Calculating Loan Payments...............1 Calculating Principal Payments...........4 Working with Future Value...............7 Using the Present Value Function..........9 Calculating Interest

### Annuities and Sinking Funds

Annuities and Sinking Funds Sinking Fund A sinking fund is an account earning compound interest into which you make periodic deposits. Suppose that the account has an annual interest rate of compounded

### PRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.

PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values

### E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is

E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =

### TIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction

TIME VALUE OF MONEY #6: TREASURY BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This problem assumes that you have mastered problems 1-5, which are prerequisites. In this

### 2 Time Value of Money

2 Time Value of Money BASIC CONCEPTS AND FORMULAE 1. Time Value of Money 2. Simple Interest 3. Compound Interest 4. Present Value of a Sum of Money 5. Future Value It means money has time value. A rupee

### Finance 331 Corporate Financial Management Week 1 Week 3 Note: For formulas, a Texas Instruments BAII Plus calculator was used.

Chapter 1 Finance 331 What is finance? - Finance has to do with decisions about money and/or cash flows. These decisions have to do with money being raised or used. General parts of finance include: -

### Solutions to Problems: Chapter 5

Solutions to Problems: Chapter 5 P5-1. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start

### Ehrhardt Chapter 8 Page 1

Chapter 2 Time Value of Money 1 Time Value Topics Future value Present value Rates of return Amortization 2 Time lines show timing of cash flows. 0 1 2 3 I% CF 0 CF 1 CF 2 CF 3 Tick marks at ends of periods,

### Student Loans. The Math of Student Loans. Because of student loan debt 11/13/2014

Student Loans The Math of Student Loans Alice Seneres Rutgers University seneres@rci.rutgers.edu 1 71% of students take out student loans for their undergraduate degree A typical student in the class of

### 6: Financial Calculations

: Financial Calculations The Time Value of Money Growth of Money I Growth of Money II The FV Function Amortisation of a Loan Annuity Calculation Comparing Investments Worked examples Other Financial Functions