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1、1,Chapter 8 Compound Interest :future value and present value,8.2 Future Value (or Maturity Value),2,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.,3,Maturity value (compound interest),(8-2),
2、p= the principal i= the interest rate per compounding period(periodic interest rate)n= the number of compounding period in the terms= the maturity value,(8-2),4,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 9.7
3、5% 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=10,5,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
4、 investment?,6,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=24,7,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.,8,Example 8.2 C Calculati
5、ng 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?,9,Solution:,months,0,18,36,P1=$5000,S1=P2,S2,9.
6、75% compounded semiannually,9.25% compounded quarterly,10,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=6,11,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 $6
7、615.44 after 3 years.,12,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 on the fourth anniversary
8、will extinguish the debt?,13,Solution:,0,1,2,3,4,P1=$5000,years,S1-$1500=P2,S2-$1500=P3,S3-$1500=P4,S4,11% compounded quarterly,14,j=11% compounded quarterly m=4 i=j/m=2.75% (per quarter) p2=s1-$1500=$4073.11,15,p3=s2-$1500=$3039.97 p4=s3-$1500=$1888.42,16,payment made on the fourth anniversary will
9、 extinguish the debt is $2104.87.,17,Comparison of maturity values at compound and simple interest,The effect of compound interest is to produce an accelerating growth in an investments values as time passes.,18,Compare the Growth of Two Investments:,$100 invested at 10% compounded annually$100 inve
10、sted at 10% pa simple interest,The components of future value,19,Figure 8.2-P294,20,For the compound interest investment,The upper curve was obtained by plotting values of S for n ranging from 0 to 10 compounding periods (year).This accelerating growth pattern known as exponential growth.The compoun
11、ding of interest causes the maturity value to increase by the same percentage (10%) each year.,21,For the simple interest investment,This gives an inclined straight line when we plot values of S for t ranging from 0 to 10 years.In this case, the future value increase $10 per year because only the or
12、iginal principal of $100 earns 10% interest each year.,22,The effect of the nominal interest rate on the future value,a, $100 earns 10% compounded annuallyb, $100 earns 12% compounded annuallyc, $100 earns 8% compounded annuallyd, $100 earns 6% compounded annually,Compare the Growth of Four Investme
13、nts:,23,24,Compare the future values after 25 years at the 10% and 12% rate.,The ratio of the total interest earnings after 25 years for 10% and 12% cases isIn comparison, the ratio of the two interest rates is only 12%/10%=1.2,bs growth is 1.63 times as growth, even though the interest rate earned
14、by b is only 1.2 times the rate earned by a.,25,The Implications for Planning and Managing Your Personal Financial Affairs Are:,You should begin an investment plan early in life to realize the dramatic effects of compounding over the long run.You should try to obtain the best available rate of retur
15、n (at your acceptable level of risk). An extra 0.5% or 1% annual rate of return has a disproportionate effect on investment growth, particularly in the long run.,26,The effect of the compounding frequency on the future value,As time passes, the higher compounding frequency produces a surprisingly la
16、rge and ever-increasing difference between the maturity values.,Figure 8.4 on page 296,27,Example 8.2E A small claims court has ruled in favour of Mrs.Peacock. She claimed that Professor Plum defaulted on two payments of $1000 each. One payment was due 18 months ago, and other 11 months ago. What is the appropriate amount for the court to order Plum to pay immediately if the court uses 6% compounded monthly for the interest rate money can earn?,
