125% S. You are one of the retireament counselons at the Valley View Bank. You h

Question

125% S. You are one of the retireament counselons at the Valley View Bank. You have been asked to give a presentation to a class of high school seniors about the importance of saving for retrement. Your boss, the vice president of the trust division, has designed an example for you to use in your presentation. The students ane shown five retirement scenarios and are asked to goess which yields the most money, Note: All annuities are ordinary the money remains in the account at 10% interest compounded annually. Although some people stop investing. Look over each scenario and make an educated guess as to which investor will have the largest accumulation of money invested at 10% over the next 40 years. Then for your presentation, calculate the final value for each scenario. Venus invests $1,200 per year and stops after 15 years Kevin waits 15 years, invests $1,200 per year for 15 years, and stops Rafael waits 15 years, then invests S1,200 per year for 25 years Magda waits 10 years, invests $1,500 per year for 15 years, and stops. Heather waits 10 years, then invests $1,500 per year for 30 years Based on the results, what message will this presentation convey to the stu dents? b. So 20 e. Recalculate each scenario as an annuity due.

Explanation / Answer

Interest rate = 10% per year

Time = 40 year

now let take one by one and calculate the final value of amt at the end of 40 years, assumption - installment amt. will be paid at the end of the year

Venus invest 1200 per year for 15 year -

at eh end of 15th year amt is in his a/c = 1200*[(1+.10)^15 -1]/.10

= 1200*(4.177-1)/.10

= 12000*3.177

= 38127

after 40 years amt. would be in his a/c = 38127*(1+.10)^25

= 413094.6

Now kevin waits for 15 year and then invest 1200 per year for 15 years and stops

amt. after 30 year = 38127(same as calculated above)

now after 40 year the amt. would be in kevin's account = 38127*(1+.10)^10

= 38127*1.59

= 98892

Rafel waits for 15 year and invest 1200 per year for 25 year

amt. will be in his account after 40 years= 1200*[(1+.10)^25-1]/.10

= 12000*(10.83471-1)

= 12000*9.83471

= 118017

for Magda -

1500*[(1+.10)^15-1]/.10

= 15000*(4.177248-1)

= 15000*3.177248

= 47659

at the end of 40 year amt would be = 47659*(1+.10)^15

= 47659*4.177248

= 199084

For heather -

amt invest 1500 for 30 year

= 1500*[(1+.10)^30-1]/.10

= 15000*16.4494

= 246741

(b) start investing as soon as you can. because in first case the amt. will be most higher compare to others however some of them invest per year more amt. for more years.

(c) For annuity due -

formula is - amt.*[(1+i)^n-1]*(1+i)/i

for venus 1200*[(1+.10)^15-1)*1.10/.10

= 12000*(4.177248-1)*1.10

= 12000*3.177248*1.10

= 41939.7

this amt. will come after 15 years after 40 years the same amt will be = 41939.7*(1+.10)^25

= 41939.7*10.83471

= 454404.3

the same calcualtion will be done for all case answer would be as follows -

in case of any problem please comment.

Annuity amt Rest period from CI Total Amt. after 40 years Venus 41939.7 412464.6 454404.3 Kevin 41939.7 66841.08 108780.8 Rafel 129818.7 0 129818.7 Magda 52424.9 166566.9 218991.8 Heather 271415.1 0 271415.1

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