Question

Answers are given but please show work

7. (2pts) April received an inheritance from her grandmother in the form of an annuity. The annuity pays annually $3000 on January 1st from 1996 through 2014. Find the value of this annuity on January 1, 1996 using an annual effective interest rate of 5%. (Answer: $38,068.76.)

8. (4pts) Susan makes deposits of $100 at the end of each year for 40 years, and her fund earns an annual effective interest rate of 8%. Starting at the end of 41 years, Susan makes an annual withdraw of X for 15 years. The fund has a balance of 0 after the last withdraw. Find X. (Answer: $3026.55.)

9. (4pts) An investment requires an initial payment of $10,000 and annual payments of $1,000 at the end of each of the first 10 years. Starting at the end of the eleventh year, the investment returns five equal annual payments of X. Determine X to yield an annual effective interest rate of 10% over the 15-year period. (Answer: $11,046.)

Answer 1

1.

=3000/5%*(1-1/1.05^19)*1.05=38068.76

2.

=100/8%*(1.08^40-1)*8%/(1-1/1.08^15)=3026.5455

3.

=(10000*1.1^10+1000/10%*(1.1^10-1))*10%/(1-1/1.1^5)=11046.48