1,Chapter 6 Simple Interest,6.2 Determining The Time Period (Term),2,Whenever possible, the time period t should be determined using the exact number of days involved . Table 6.1Month Days Month DaysMonthDaysJanuary 31 May31September30February 28 June30October31March 31 July31November30April 30 August 31 December31,3,Example: Find the exact number of days from January 23,1994 to June 7,1994,number of days =(31-23+1)+28+31+30+31+6 1 2 3 4 5 6 =135 days,Solution:,4,5,Example6.2A: Calculating And Using The Exact Number of Days,A, Calculate the term for each of the following loans. Loan Date Date Interest principal advanced repaid rate pa (1)$3,000 March 31,1997 September 4,1997 (2)$23,000 November 29,1997 April 1,1998 13.4% (3)$14,600 January 11,1996 June 4,1996 B, Calculate the interest due on the repayment date for each loan.,6,Solution:,A, We calculate the term with two methods, respectively. Method 1 use table 6.1 , and Method 2 use table 6.2.,7,(1) From March 31 ,1997 to September 4, 1997,The number of days=1+30+31+30+31+31+3=157 Date Day numberSeptember 4,1997 247March 31, 1997 -90 =157,Method 1,Method 2,The exact numberof days is 157.,8,(2) November 29,1997 to April 1,1998,The number of days=2+31+31+28+31+0=123 daysDate Day numberDecember 31,1997 365November 29,1997 -333 32April 1,1998 +91 =123,Method 2,The exact numberof days is 123.,Method 1,9,(3) January 11,1996 to June 4,1996,the number of days=21+29+31+30+31+3=145 daysDate Day numberJune 4 (general) 155 +1June 4,1996 156January 11,1996 -11Time period 145,The exact numberof days is 145.,Method 2,Method 1,10,B Calculate Interest,(1)term = 157days r= p=$3000I=prt=$ 164.53,(2)term = 123days r= 13.4% p=$23,000I=prt=$ 1038.59,(3)term = 145days r= p=$14,600I=prt=$ 826.5,11,When a loans interest rate is linked to the prime rate charged by the chartered banks, it is described as a variable interest rate or a floating interest rate.,The prime rate of interest is the banks lowest lending rate.,12,EXAMPLE 6.2B Variable Interest Rate,Winston borrowed $5000 on April 7. The interest rate was tied to the prime lending rate and consequently it changed whenever the prime lending rate changed. The interest rate was initially 10.5%pa. It increased to 11%pa effective May 23, and to 11.25% pa effective July 13. What amount was required to repay the loan on August 2?,13,Interval Number Interest Interest of days rate April 7 to May 23 24+22=46 10.50% $66.16 May 23 to July 13 9+30+12=51 11.00% $76.85 July 13 to August 2 19+1=20 11.25% $30.82 Total $173.83 The amount required to repay the loan on August 2 was $5000+$173.83=$5173.83.,