Question

Problem 4-48 Calculating Present Values A 4-year annuity of eight $9,800 semiannual payments will begin 7 years from now, with the first payment coming 7.5 years from now. a. If the discount rate is 7 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. If the discount rate is 7 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. If the discount rate is 7 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Number of Periods of annuity =8
Effective semi annual rate = (1+APR/12)^6 =(1+7%/12)^6-1 =3.55144039829847%
Value of annuity 7 years from now =PMT*(1-(1+r)^-n)/r
=9800*((1-(1+3.55144039829847%)^-8)/3.55144039829847%)=67220.373874

Value of annuity 5 years from now =67220.373874/(1+7%/12)^24=58462.36
Value 5 years from now I/Y=3.55144039829847%;N=24; FV=-67220.373874;CPT PV=58462.36

Value of annuity 3 years from now =67220.373874/(1+7%/12)^48=50845.41
Value of annuity 3 using financial calculator
I/Y=3.55144039829847%;N=48;FV=-67220.372874;CPT PV =50845.41

Value of annuity now =67220.373874/(1+7%/12)^84=41239.64
Value of annuity now using financial calculator
I/Y=3.55144039829847%;N=72;FV=-67220.372874;CPT PV =50845.41