Future Value (or Maturity Value)参考.ppt

Chapter 8 Compound Interest :future value and present value 8.2 Future Value (or Maturity Value) Calculating the Future Value The maturity value or future value is the combined principal and interest due at the maturity date of a loan or an investment. Maturity value (compound interest) Example 8.2 A Calculating The Maturity Value Of A Lump Investment What will be the maturity value of $10,000 invested for five years at 9.75% compounded semiannually? Solution: p=$10,000 term =5 years j=9.75% pa m=2 i=j/m=9.75%/2=4.875% n=m*term=10 Example 8.2 B Comparing Two Nominal Rates of Interest Other things being equal, would an investor prefer an interest rate of 10.5% compounded monthly or 11% compounded annually for a 2-year investment? Solution: When interest rate is 10.5% compounded monthly. j1=10.5% m1=12 i1=10.5%/12=0.875% (per month) p=$1000 n1=24/1=24 When interest rate is 11% compounded annually j2=11% m2=1 i2=11% n2=2 p=$1000 s1s2, so the preferred rate is 10.5% compounded monthly. Example 8.2 C Calculating the Maturity Value When the Interest Rate Changes George invested $5000 at 9.25% compounded quarterly. After 18 months, the rate changed to 9.75% compounded semiannually. What amount will George have accumulated 3 years after the initial investment? Solution: From 0 to 18 months j1=9.25% compounded quarterly m1=4 i1=9.25%/4=2.3125% (per quarter) p1=$5000 n1=18/3=6 From 18 to 36 months p2=S1=$5735.12 n2=18/6=3 j2=9.75% compounded semiannually m2=2 i2=9.75%/2=4.875% George will have accumulated $6615.44 after 3 years. Example 8.2 D The Balance Owed After Payments on a Compounded Interest Loan Fay borrowed $5000 at an interest rate of 11% compounded quarterly. On the first, second, and third anniversaries of the loan, she made payments of $1500. What payment made o