McGraw-Hill Ryerson© Simple Interest Simple Interest Chapter 6 McGraw-Hill Ryerson© I I S S imple nterest

McGraw-Hill Ryerson© Simple Interest Simple Interest Calculate Learning Objectives After completing this chapter, you will be able to: … interest, maturity value, future value, and present value in a simple interest environment … details of the amount and timing of payments in a time diagram … the equivalent value on any date of a single payment or a stream of payments, and Present LO-1 LO-2

McGraw-Hill Ryerson© Simple Interest Simple Interest Borrower Example: Loan Lender Parties Lends the Principal Borrower OWES (Debt) to Lender Borrower OWES (Debt) to Lender LO-1

McGraw-Hill Ryerson© Simple Interest Simple Interest Borrower Lender Earns (Income) from Borrower i.e. Interest on the Principal Borrower pays Interest to Lender Rate of Interest: Simple Interest … Calculated on an ANNUAL or per annum (pa) basis Simple Interest … Calculated on an ANNUAL or per annum (pa) basis Example: Loan

McGraw-Hill Ryerson© Simple Interest Simple Interest Examples Invest $1000 at 10% simple interest for one year. Interest earned is? Principal X Interest Rate $1000 * 10% = $100 Invest $1000 at 10% simple interest for six months. Interest earned is? Principal X Interest Rate $1000 * 10% $50 /2 =/2 = = =

McGraw-Hill Ryerson© Simple Interest Simple Interest Invest $1000 at 10% simple interest for three months Interest earned is? Principal X Interest Rate = $1000 X 10% $25 Invest $1000 at 10% simple interest for one month. Interest earned is? Principal X Interest Rate = $1000 X 10%$8.33 / 12 = / 4 = Examples

McGraw-Hill Ryerson© Simple Interest Simple Interest Up to this point we have taken months to represent 1/12 th of a year, i.e. each month is treated as having the same number of days! Would it not be more accurate to calculate the interest due or payable based on the actual number of days in each month?

McGraw-Hill Ryerson© Simple Interest Simple Interest Yes, it would! In fact, interest continues to accumulate as each day passes! Invest $1000 at 10% simple interest for 30 days! Interest earned is? Example Principal x Interest Rate = $1000 * 10% * 30 Year = 365 days or 366 in a Leap Year $8.22 = 365

McGraw-Hill Ryerson© Simple Interest Simple Interest tr PI What is the formula that can be used to calculate SI? PrincipalInterest RateTime Four Elements are involved … Interest Formula Principal Amount (loan or investment) Principal Amount (loan or investment) Annual Rate of SI Annual Rate of SI Amount (paid or received) Amount (paid or received) Time period …expressed as a fraction or a multiple of a year I =PrtPrt

McGraw-Hill Ryerson© Simple Interest Simple Interest Calculate the Interest earned on $5000 invested at 4% for 7 months. Formula I =PrtPrt P *r *t $5000 *.04 * 7 /12 I = $116.67

McGraw-Hill Ryerson© Simple Interest Simple Interest I may need to invest or need a loan for a number of days rather than a complete month. How do I calculate the time between the starting date and the ending date ?

McGraw-Hill Ryerson© Simple Interest Simple Interest Formula I =PrtPrt Calculate the Interest earned on $5000 invested at 4.5% for ?. 79 Days I = $5000 *.045 * 79/365 I = $48.70

McGraw-Hill Ryerson© Simple Interest Simple Interest Formula I =PrtPrt $5000 *.045 * 37/365 I = $22.81 Calculate the Interest earned on $5000 invested at 4.5% for ?. 37 Days

McGraw-Hill Ryerson© Simple Interest Simple Interest Formula I =PrtPrt $5000 *.04 * 151/365 I = $82.74 Calculate the Interest earned on $5000 invested at 4.0% for ?. 151 Days