The equivalent value of a payment stream参考.ppt

Chapter 6 Simple Interest 6.5 The equivalent value of a payment stream Payment stream: is a series of two or more payments required by a single transaction or contract. The original or old set of debts or obligations must have the same equivalent value as the equivalent value of the new set of payments at the same focal date. EXAMPLE: Lia had agreed to pay Kemuel $4000 in five months, she has just received some extra money and would like to pay him $2000 one month from now, and make a final payment in four months. What will the final payment be if they agree to use 7% simple interest and a focal date of four months from now? Solution: 0 represent now. Use X representing the final payment. Owing =$4000 due in five months Paying =$2000 in one month and a payment in 4 months that can be called x Substituting in S+X=P, we get X= $1941.80 The unknown payment due in four months is $1941.80. Example 6.5 A Calculating a Payment Equivalent to Three Scheduled Payments A financial obligation was supposed to be settled by payments of $1000 on a date 2 months ago, $2000 today, and $3000 on a date 6 months from now. The creditor has agreed to accept a single equivalent payment 2 months from now instead of the scheduled payments. If money can earn 6% pa, what will be the size of the equivalent payment? Solution: Example 6.5 B Calculating A Payment Equivalent To Interest-earning Obligations Four months ago Darren borrowed $1000 from Sean and agreed to repay the loan in two payments to be made 5 and 10 months after the date of the agreement. Each payment is to consist of $500 of principal, and interest at the rate of 9% pa on that $500 from the date of the agreement. Today Darren is asking Sean to accept instead a single payment 3 months from now to settle the debt. What payment should Sean require if money can now earn 7% pa? Solution: S1 =the future value of $500