Question

You deposit $11,000 annually into a life insurance fund for the next 10 years, after which time you plan to retire. a. If the deposits are made at the beginning of the year and earn an interest rate of 7 percent, what will be the amount in the retirement fund at the end of year 10? b. Instead of a lump sum, you wish to receive annuities for the next 20 years (years 11 through 30). What is the constant annual payment you expect to receive at the beginning of each year if you assume an interest rate of 7 percent during the distribution period? c. Repeat parts (a) and (b) above assuming earning rates of 6 percent and 8 percent during the deposit period and earning rates of 6 percent and 8 percent during the distribution period.

Answer 1

B 4 a) 5 interest rate 6 future value interest rate factor of annuity 0.07 13.81645 8 future value 162619.59 9 20 10 b) 11 period of distribution 12 present value interest rate factor of annuity 10.59401 13 present value for beginning of the year payı 174003 14 amount per year 16424.65 15 16 c) 17 interest rate 6% 18 future value interest rate factor of annuity 13.18079 14.48656 8% 19 20 future value 153688.07 172100.36 27 23 period of distribution 20 20 24 present value interest rate factor of annuity 11.46992 9.818147 25 present value for beginning of the year payı 162909.4 185868.4 26 amount per year 14203.18 18931.11 27

0.07 =(((1+B5)^$B$2)-1)/B5 =$B$1*(1+B5)*B6 20 =(((1+B5)^$B$11)-1)/(((1+B5)^$B$11) *B5) =B8*(1+B5) =B13/B12 4 a) 5 interest rate 6 future value interest rate factor of annuity 7 8 future value 9 10 b) 11 period of distribution 12 present value interest rate factor of annuity 13 present value for beginning of the year payments 14 amount per year 15 16 C) 17 interest rate 18 future value interest rate factor of annuity 19 20 future value 21 22 23 period of distribution 24 present value interest rate factor of annuity 25 present value for beginning of the year payments 26 amount per year 27 0.06 =(((1+B17)^$B$2)-1)/B17 0.08 =(((1+C17)^$B$2)-1)/C17 =$B$1*(1+B17)*B18 =$B$1*(1+C17)*C18 20 20 =[((1+B17)^$B$11)-1)/(((1+B17)^$B$11) *B17) =(((1+C17)^$B$11)-1)/(((1+C17)^$B$11)*C17) =B20*(1+B17) =C20*(1+C17) =B25/B24 =C25/C24