# Copyright © 2008 Pearson Education Canada 7-1 Chapter 7 Interest.

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Copyright © 2008 Pearson Education Canada 7-1 Chapter 7 Interest

Copyright © 2008 Pearson Education Canada 7-2 Chapter 7 Interest Important Lenders Provides a return on funds lent out Borrowers Costs of having right to access funds temporarily

Copyright © 2008 Pearson Education Canada 7-3 Time Value of Money Basic concept in personal finance Essential to understanding Annuities Insurance Pensions Bonds

Copyright © 2008 Pearson Education Canada 7-4 Time Value of Money Economic value of money Depends on when it is paid A dollar paid today has a larger economic value Than a dollar paid ten years from now Money has time value Because of the rate of return it earns Interest

Copyright © 2008 Pearson Education Canada 7-5 Interest Fee lenders charge For use of their money Income to the lender Expense to the borrower

Copyright © 2008 Pearson Education Canada 7-6 Interest Calculations With Lump-sum Payments

Copyright © 2008 Pearson Education Canada 7-7 Two Systems to Calculate Interest Simple interest Compound interest

Copyright © 2008 Pearson Education Canada 7-8 Simple Interest Short-term investments and loans Less than one year duration Principal and interest repaid Lump-sum Specified time

Copyright © 2008 Pearson Education Canada 7-9 3 Things Determine Amount of Simple Interest 1. Principal 2. Rate 3. Time

Copyright © 2008 Pearson Education Canada 7-10 1. Principal Amount loaned Investment To the lender Amount borrowed Debt To the borrower

Copyright © 2008 Pearson Education Canada 7-11 2. Rate Expressed as Annual rate Per annum rate

Copyright © 2008 Pearson Education Canada 7-12 3. Time The term Expressed in Years

Copyright © 2008 Pearson Education Canada 7-13 Simple Interest Calculation

Copyright © 2008 Pearson Education Canada 7-14 Calculating Amount of Interest What amount of interest will be charged on \$2,500 for 7 months at a simple interest rate of 8%?

Copyright © 2008 Pearson Education Canada 7-15 Calculating the Amount of Principal At a simple rate of interest of 4.25%, how much must be deposited in a bank for 9 months to earn \$200 of interest?

Copyright © 2008 Pearson Education Canada 7-16 Calculating the Interest Rate What simple rate of interest was charged on a loan of \$3,800 for 10 months if the amount of interest was \$195.25?

Copyright © 2008 Pearson Education Canada 7-17 Calculating the Term What is the term in months of an investment of \$5000, that earned interest of \$243.75 at a rate of 6.50%?

Copyright © 2008 Pearson Education Canada 7-18 Calculating Future Value Maturity value Combine principal and interest due At maturity date Denoted as S in the formula

Copyright © 2008 Pearson Education Canada 7-19 Calculating Future Value What is the maturity value of an investment of \$1200.67 for 11 months at a simple interest rate of 5.75%?

Copyright © 2008 Pearson Education Canada 7-20 Compound Interest Investments and loans More than one year duration Interest calculated periodically Interest converted to principal periodically Interest added to principal Thereafter treated as principal

Copyright © 2008 Pearson Education Canada 7-21 Future Value of a Lump Sum Calculating maturity value Of a lump sum Deposited today

Copyright © 2008 Pearson Education Canada 7-22 Calculating Future Value of a Lump Sum FV = future value PV = present value n = total number of compoundings i= rate of interest

Copyright © 2008 Pearson Education Canada 7-23 Calculating Future Value of a Lump Sum What will be the future value of \$4,900 invested at 4.25% compounded semiannually for five years?

Copyright © 2008 Pearson Education Canada 7-24 Present Value of a Lump Sum Calculating today’s value Of a lump sum To be received at some future date

Copyright © 2008 Pearson Education Canada 7-25 Calculating Present Value of a Lump Sum

Copyright © 2008 Pearson Education Canada 7-26 Calculating Present Value of a Lump Sum How much must you invest today in order to accumulate \$30,000 in six years, if you can earn 3.75% compounded monthly?

Copyright © 2008 Pearson Education Canada 7-27 Interest Calculations With a Series of Payments

Copyright © 2008 Pearson Education Canada 7-28 Annuity Series of equal payments At regular intervals Examples Rent payment Mortgage payment Pension benefit

Copyright © 2008 Pearson Education Canada 7-29 Future Value of an Annuity Sum of the future values Of each payment Evaluated at end of the last payment interval

Copyright © 2008 Pearson Education Canada 7-30 Calculating Future Value of an Annuity

Copyright © 2008 Pearson Education Canada 7-31 Future Value of Periodic Investments You plan to contribute \$75 at the end of each month to an education plan that earns 5% compounded monthly. How much will you have 17 years from now?

Copyright © 2008 Pearson Education Canada 7-33 Calculating the Periodic Investment to Reach a Target Calculate the amount you have to invest at the end of each month, at 6.5% compounded monthly, to have \$700,000 in your RRSP in 31 years’ time.

Copyright © 2008 Pearson Education Canada 7-35 Present Value of an Annuity Sum of the present values Of each payment Evaluated at beginning of the first payment interval

Copyright © 2008 Pearson Education Canada 7-36 Calculating Present Value of an Annuity

Copyright © 2008 Pearson Education Canada 7-37 Calculating the Amount to Fund an Annuity If money earns 6% compounded monthly, how much money is required to fund an annuity of \$2,500 at the end of each month for 30 years?

Copyright © 2008 Pearson Education Canada 7-39 Calculating a Periodic Loan Payment A \$20,000 loan requires payments at the end of each month for 3 years. If the interest rate is 9% compounded monthly, what is the size of each payment?