McGraw-Hill Ryerson © Applications SI Applications SI A pplications of McGraw-Hill Ryerson © Chapter 7 I I S S imple nterest

McGraw-Hill Ryerson © Applications SI Applications SI Calculate Learning Objectives After completing this chapter, you will be able to: …the MARKET PRICE and rate of return for Treasury Bills and Commercial Paper …Interest paid on Savings Accounts, Term Deposits, and Guaranteed Investment Certificates also… LO-1 LO-2

McGraw-Hill Ryerson © Applications SI Applications SI State …the Valuation Principle and apply it to the calculation of the Fair Market Value of an investment providing specified future cash flows …typical terms, conditions, and repayment arrangements for revolving ( demand ) loans, fixed-payment (demand) loans, and Canada Student Loans Describe the… Learning Objectives LO-3 LO-4

McGraw-Hill Ryerson © Applications SI Applications SI N otes about … avings Accounts S hort -Term GICs LO-1

McGraw-Hill Ryerson © Applications SI Applications SI Interest About often calculated on daily balance and posted monthly avings Accounts

McGraw-Hill Ryerson © Applications SI Applications SI G uaranteed I nvestment C ertificates 30 – 364 day terms “Guaranteed” refers to the unconditional guarantee of principal and interest by the parent financial institution. S hort -Term GICs About and…

McGraw-Hill Ryerson © Applications SI Applications SI Non- Redeemable - Redeemable (or cashable GIC or term deposit) Non- Redeemable Redeemable (or cashable GIC or term deposit) Can be “ cashed in ” before maturity date Most GICs are not redeemable before maturity Cannot be “ cashed in ” before maturity date S hort -Term GICs About also…

McGraw-Hill Ryerson © Applications SI Applications SI Can be purchased from banks, credit unions, trust companies, and caisses populaires (in Quebec). (you are in effect lending money to the financial institution) The financial institution uses the funds raised from selling GICs to make loans … most commonly, mortgage loans S hort -Term GICs About also…

McGraw-Hill Ryerson © Applications SI Applications SI …Higher rates are paid for longer terms (within the 30 to 364-day range) …Higher rates are paid on non-redeemable GIC’s …Higher rates are paid on larger principal amounts …Mortgage rates are typically 1.5% to 2% higher than the interest rate paid to GIC investors. S hort -Term GICs About

McGraw-Hill Ryerson © Applications SI Applications SI S hort -Term GICs About

McGraw-Hill Ryerson © Applications SI Applications SI Case 1 For amounts of $5000 to $99,999 and terms of 90 to 179 days, the Royal Bank pays an interest rate of 2.80% pa on redeemable GICs and 3.15% on non-redeemable GICs. S hort -Term GICs About

McGraw-Hill Ryerson © Applications SI Applications SI In order to retain the redemption privilege, how much Interest (in dollars) must be sacrificed on an investment of $15,000 for 120 days ? S hort -Term GICs About

McGraw-Hill Ryerson © Applications SI Applications SI Non-redeemable GIC Redeemable GIC I = * = $ = $ * 120 / * 120 / 365 Interest Sacrifice $17.26 Subtract S hort -Term GICs

McGraw-Hill Ryerson © Applications SI Applications SI For amounts between $10,000 and $24,999, a bank pays a rate of 4.5% on GICs with maturities in the 91 to 120-day range. However, early redemption will result in a rate of 3% being applied. Case 2 S hort -Term GICs

McGraw-Hill Ryerson © Applications SI Applications SI How much more Interest will a 120-day $22,000 GIC earn if it is held until maturity than if it is redeemed after 100 days ? S hort -Term GICs

McGraw-Hill Ryerson © Applications SI Applications SI Days 100 Days I = * = $ = $ * 120 / * 100 / 365 More Interest $ Subtract S hort -Term GICs 4.5% 3.0% for early

McGraw-Hill Ryerson © Applications SI Applications SI LO-2 Applications SI Applications SI

McGraw-Hill Ryerson © Applications SI Applications SI Paper contracts issued to lenders by the federal government and several provincial governments when they borrow money for terms of less than one year. …the FACE VALUE (Maturity Value) of a T-Bill includes the Interest that the T-bill will earn during its life ! Treasury Bills

McGraw-Hill Ryerson © Applications SI Applications SI Find the price of a 91-day $75,000 T-bill on its date of issue if the going rate of interest is 5.1%. PV = $75,000/[1+(0.051*91/365)] = $74, Treasury Bills

McGraw-Hill Ryerson © Applications SI Applications SI Suppose that the institutional purchaser of the T-bill in the previous example sells it to a client on the same day at a higher price that represents a lower yield to the client of 4.6%. What profit did the institution make on the transaction? Treasury Bills

McGraw-Hill Ryerson © Applications SI Applications SI What profit did the institution make on the transaction? Selling Price $75000/[ (91/365)] Profit = $74, $74, Selling Price 74, Acquisition Price $ Treasury Bills

McGraw-Hill Ryerson © Applications SI Applications SI Suppose the client who purchased the 91-day, $75,000 T-bill in the previous example for $74,149.62, sold the T-bill after 30 days in order to invest the proceeds elsewhere! (a) What price would she receive if the short-term interest rate for this maturity had fallen to 4.2% by the date of the sale? Treasury Bills

McGraw-Hill Ryerson © Applications SI Applications SI (a) What price would she receive if the short-term interest rate for this maturity had fallen to 4.2% by the date of the sale? Determine the number of days remaining to maturity Calculate the Selling Price based on the Discounted Rate of 4.2% Treasury Bills

McGraw-Hill Ryerson © Applications SI Applications SI Determine the number of days remaining to maturity …purchased (T-Bill) ……. 91-day …sold (T-Bill) after ………. 30 days = 61 days PV of $75,000 discounted at 4.2% for 61 days Calculate the Selling Price based on the Discounted Rate of 4.2% = $75000/[ (61/365)] SP = $74, Treasury Bills

McGraw-Hill Ryerson © Applications SI Applications SI Suppose the client who purchased the 91-day, $75,000 T-bill in the previous example for $74,149.62, sold the T-bill after 30 days in order to invest the proceeds elsewhere! (b) What Rate of Return (per annum) did the client realize while holding the T-bill? Treasury Bills

McGraw-Hill Ryerson © Applications SI Applications SI , $74, (b) What Rate of Return (per annum) did the client realize while holding the T-bill? …Purchased (T-Bill) ……. …Sold (T-Bill) after 30 days Grew in 30 Days by… $ I PrtPrt r = I / Pt r = / = = 5.38% Treasury Bills 74, (30/365)

McGraw-Hill Ryerson © Applications SI Applications SI The Valuation Principle LO-3 Applications SI Applications SI

McGraw-Hill Ryerson © Applications SI Applications SI …the Fair Market Value of an investment and is the Sum of the Present Value(PV) of the expected cash flows The Discount Rate used in the Present Value(PV) calculations should be the Market-determined Rate of Return required for this type of investment The Valuation Principle

McGraw-Hill Ryerson © Applications SI Applications SI Consider an investment that will deliver a single payment of $110 one year from now. What is the most you should pay to buy the investment if you require a minimum return of 10%? The Valuation Principle

McGraw-Hill Ryerson © Applications SI Applications SI $110 one year from now = Future Value(FV) $110 represents 110%or 100% + 10% Return We are looking for the Present Value $100 is the most you should pay = $100 = The Valuation Principle 110/[1+0.10*(1)] PV = FV / ( 1 +rt)

McGraw-Hill Ryerson © Applications SI Applications SI The process of calculating a payment’s Present Value is often called “Discounting the payment” The Valuation Principle

McGraw-Hill Ryerson © Applications SI Applications SI The Valuation Principle Applications SI Applications SI

McGraw-Hill Ryerson © Applications SI Applications SI An investment promises two payments of $2000, on dates 1 and 4 months from now. What price will an investor pay today if the required rate of return is 8% ? 1 month = 1/12 4 months = 4/12 (1) Using a Time Line display, and (2) Both algebraically and by calculator (1) Using a Time Line display, and (2) Both algebraically and by calculator The Valuation Principle Formula = FV / ( 1 +rt) PV

McGraw-Hill Ryerson © Applications SI Applications SI PV= $ = /[1+0.08*(1/12)] 2000/[1+0.08*(4/12)] = (1) $2000 Months Months Present Value PV (2) + The Valuation Principle

McGraw-Hill Ryerson © Applications SI Applications SI PV= $ = = /[1+0.08*(1/12)] /[1+0.08*(4/12)] Today’s Value: = The Valuation Principle

McGraw-Hill Ryerson © Applications SI Applications SI LO-4 Applications SI Applications SI

McGraw-Hill Ryerson © Applications SI Applications SI About … Loans where the lender has the right to demand full repayment of the loan at any time! …revolving loans … fixed payment loans

McGraw-Hill Ryerson © Applications SI Applications SI About... Borrower may repay any portion of the loan at any time without penalty … Interest rate charged is usually “floating” … Interest is calculated on the same ‘statement date’ each month … Interest is calculated up to but not including the statement date

McGraw-Hill Ryerson © Applications SI Applications SI The debt was completely repaid on June 30 together with the accrued interest. What was (a) the total interest charge, and (b) the total payment on June 30? You negotiated a $5000 demand loan on March 1 at prime plus 2%. The prime rate was 5% on March 1 and decreased to 4% on May 18. On May 20 you paid $1225 towards principal plus the accrued interest.

McGraw-Hill Ryerson © Applications SI Applications SI Determine the number of days in each period Calculate the interest accrued to date of payment Record the information provided and known in a Table format Calculate the balance after the payment Calculate the interest accrued and the final balance on June 30

McGraw-Hill Ryerson © Applications SI Applications SI Date Interest Accrued Paid 5, Balance $ Mar 1 May18 May 20 June Record the information that is known! Days Interest Rate TotalPrimePlus

McGraw-Hill Ryerson © Applications SI Applications SI Determine the number of days in each period Look up Days Look up Days DatePrimePlus Interest Accrued Paid 5, Balance $ Mar 1 May18 May 20 June Total Interest Rate Days

McGraw-Hill Ryerson © Applications SI Applications SI Calculate the interest accrued …Calculation DatePrimePlus Interest Accrued Paid 5, Balance $ Mar 1 May18 May 20 June Total Interest Rate Days

McGraw-Hill Ryerson © Applications SI Applications SI Calculate the interest accrued $5000 * 0.07 * 78/365 $5000 * 0.06 * 2/365 = $76.48 = $ 1.64 Total = $ Interest Accrued Days I R Total 6.0 Date Mar 1 May18 May 20 June 30 $76.48 $ 1.64 Balance $5000 …complete the Table

McGraw-Hill Ryerson © Applications SI Applications SI DatePrimePlus Interest Accrued Paid 5, Balance $ Mar 1 May18 May 20 June Total Interest Rate Days Payment $1, Interest , , , , Calculate the balance after the payment

McGraw-Hill Ryerson © Applications SI Applications SI Interest Accrued = $3, *.06 * 41/365 = $ DatePrimePlus Interest Accrued Paid 5, Balance $ Mar 1 May18 May 20 June Total Interest Rate Days 5, , , , Calculate the interest accrued and final balance on June ,800.44

McGraw-Hill Ryerson © Applications SI Applications SI You completed your college programme in December. On June 30, you paid all of the interest that had accrued (at prime +2.5%) on your $5800 Canada Student Loan during the six-month grace period. You selected the fixed rate option (prime+5%) and agreed to make end-of-month payments of $95 beginning July31. The prime rate began the grace period at 6% and rose by 0.5% effective March 29. On August 13, the prime rate rose another 0.5%. to use…

McGraw-Hill Ryerson © Applications SI Applications SI Determine the number of days in the grace period Calculate the interest accrued during the grace period Record the information provided and known in a Table format (a) Calculate the total interest paid in the first two regular payments (b) Calculate the balance after the second payment

McGraw-Hill Ryerson © Applications SI Applications SI Date Interest Accrued Paid 5, Balance $ Dec 31 Mar 29 June 30 July Record the information that is known! Days Aug 13 Aug Interest Rate TotalPrimePlus End of Grace Period

McGraw-Hill Ryerson © Applications SI Applications SI Date Interest Accrued Paid 5, Balance $ Dec 31 Mar 29 June 30 July Days Aug 13 Aug Interest Rate TotalPrimePlus End of Grace Period Determine the number of days in each period Look up Days Look up Days Interest includes June 30 due to grace period July 1

McGraw-Hill Ryerson © Applications SI Applications SI Calculate the interest accrued during the grace period …Calculation Date Interest Accrued Paid 5, Balance $ Dec 31 Mar 29 June 30 July Days Aug 13 Aug Interest Rate TotalPrimePlus End of Grace Period

McGraw-Hill Ryerson © Applications SI Applications SI Days Date Dec 31 Mar 29 June 30 July 31 Aug 13 Aug 31 IRIR Total End of Grace Period Calculate the interest accrued during the grace period Balance $5800 $5800 * * 88/365= $5800 * 0.09 * 93/365= $ $ Total = $ Interest Accrued …complete the Table Includes June 30

McGraw-Hill Ryerson © Applications SI Applications SI Calculate the interest accrued during the grace period , , , Date Interest Accrued Paid 5, Balance $ Dec 31 Mar 29 June 30 July Days Aug 13 Aug Interest Rate TotalPrimePlus End of Grace Period

McGraw-Hill Ryerson © Applications SI Applications SI …Calculation (a) , , , Date Interest Accrued Paid 5, Balance $ Dec 31 Mar 29 June 30 July Days Aug 13 Aug Interest Rate TotalPrimePlus End of Grace Period Calculate the total interest paid in the first two regular payments

McGraw-Hill Ryerson © Applications SI Applications SI First Payment $95.00 July 1 - July 31 interest $5800 *.115 * 30/365 = $54.82 Second Payment $95.00 July 31 - August 13 interest $ *.115 * 13/365 = $23.59 August 13 - August 31 interest Balance $ Add: Interest Less: Payment Balance Add: Interest Interest Less: Payment Balance $ *.12 * 18/365 = $34.09 …complete the Table Calculate the total interest paid in the first two regular payments (a)

McGraw-Hill Ryerson © Applications SI Applications SI , , , Date Interest Accrued Paid 5, Balance $ Dec 31 Mar 29 June 30 July Days Aug 13 Aug Interest Rate TotalPrimePlus End of Grace Period …the total interest paid and the balance after the second payment (a) & (b) , , , Total Interest $112.50

McGraw-Hill Ryerson © Applications SI Applications SI This completes Chapter 7