solving for the number of compounding period, n参考.ppt

Chapter 9 Compound Interest: Further Topics and Applications 9.2 solving for the number of compounding period, n Algebraic method: Financial Calculator Method: Noninteger value for n Sometimes an investment or a loan has a term that isn’t an integer number of compounding periods. In such cases, n is a noninteger. It includes the decimal fraction for the last partial compounding period. But the procedures are the same as for integer values of n. The algebraic method and financial calculator method work with both integer and noninteger values for n. Example 9.2 B Calculating and Interpreting a Noninteger n Rounded to the nearest month, how long will it take a city’s population to grow from 75,000 to 100,000 if the annual growth rate is 2%? Solution: p=75,000 s=100,000 j=i=2% Rounded to the nearest month, it will take 14 years and 6 months for the city’s population to reach 100,000. Example 9.2 E A financial contract guaranteed the payment of $4000 plus interest at a fixed rate of 9.6% compounded quarterly 2 years after the contract’s date of issue. Sometime before the maturity date, the original owner sold the contract for $4327.70. The sale price represented the fair market value given the market rate of 8.5% compounded semiannually for similar maturities. How long before the maturity date did the sale take place? Solution: Step 1: calculate the maturity value of $4000 when the contract maturity Term=2 years j=9.6% m=4 i=j/m=2.4% n=2*4=8 p=$4000 Step 2: determine how long it was before the maturity date that $4327.70 was the present value of the maturity value. j=8.5% m=2 i=j/m=4.25% p=$4327.70 s=$4835.70 Example 9.2 A stripped bond residue having a $10,000 face value was purchased for $3142.31. At this price, the bond residue provided the investor with a return of 7.938% compounded semiannually until its maturity. How long before the maturity date