1、1,Chapter 8,Compound interest: future value and present value,8.3 present value,2,Present value formula applies to two types of problems : Calculating the initial principal, and Calculating the present value.,3,The process of calculating a payments present value is described as discounting a payment

2、. The interest rate used in the present value calculation is then referred to as the discount rate.,In terms of numerical values, present value is smaller than the payment, and future value is larger than the payment. However, these numerically different amounts all have the same economic value.,4,E

3、xample 8.3A: If an investment can earn 4% compounded monthly, what amount must you invest now in order to accumulate $10,000 after 3.5 years? Solution: j=4% m=12 FV=$10,000 term=3.5 years i=j/m=0.33333% n=12*3.5=42,5,Example 8.3B,Mr. and Mrs.Espedidos property taxes, amounting to $2450, are due on J

4、uly 1. What amount should the city accept if the taxes are paid 8 months in advance and the city can earn 6% compounded monthly on surplus funds?,6,Solution:,j=6% compounded monthly m=12 i=6%/12=0.5% FV=$2450 n=8 The city should be willing to accept $2354.17 on a date 8 months before the scheduled d

5、ue date.,7,Example 8.3C,Two payments of $10,000 each must be made 1 year and 4 years from now. If money can earn 9% compounded monthly, what single payment 2 years from now would be equivalent to the two scheduled payments?,8,Solution:,year,0,2,1,4,3,S2=$10,000,P1=$10,000,Focal date,P2,S1,j=9% compo

6、unded monthly,now,9,P1=$10,000 j=9% compounded monthly m=12 i=j/m=0.75% term=1 year n1=12,S2=$10,000 i=0.75% term=2 year n2=24,The single equivalent payment on focal date will be S1+P2=$19,296.38.,10,A general principle regarding the present value of loan payments,The sum of the present values of al

7、l of the payments required to pay off a loan is equal to the original principal of the loan. The discount rate for the present-value calculations is the rate pf interest charged on the loan.,11,Example 8.3E Kamer borrowed $4000 from George at an interest rate of 7% compounded semiannually. The loan

8、is to be repaid by three payments. The first payment $1000 is due 2 years after the date of the loan. The second and third payments are due 3 and 5 years, respectively, after the initial loan. Calculated the amounts of the second and third payments if the second payment is to be twice the size of the third payment.,12,Solution:,year,0,2,5,3,x,$1000,P2,P1,j=7% compounded semiannually,2x,P3,The loan=P1+P2+P3,13,P1: n1=4,P2: n2=6,j=7% compounded semiannually i=7%/2=