You are celebrating your 35th birthday today and you want to start saving for yo

Question

You are celebrating your 35th birthday today and you want to start saving for your retirement at age 65. You want to be able to withdraw $15000 per year on each birthday for 12 years following your retirement; the first withdrawal will be on your 66th birthday. You intend to invest your money in an account that pays 9% per year. You want to make equal, annual payments on each birthday into this account. a) If you start making these deposits on your 36th birthday and continue until you are 65, what amount must be deposited annually to reach your goal? b) Suppose you just inherited a large sum of money. Rather than making equal annual payments, you decide to make one lump sum payment on your 36th birthday to cover your retirement needs. What amount do you need to deposit? c) Suppose your employer will contribute $250 into the account every year. In addition, you expect $10,000 distribution from a family trust fund on your 55th birthday, which you will also put into the retirement account. What amount do you need to deposit annually now to meet your retirement goal?

Explanation / Answer

You are celebrating your 35th birthday today and you want to start saving for your retirement at age 65. You want to be able to withdraw $15000 per year on each birthday for 12 years following your retirement; the first withdrawal will be on your 66th birthday. You intend to invest your money in an account that pays 9% per year. You want to make equal, annual payments on each birthday into this account.

a) If you start making these deposits on your 36th birthday and continue until you are 65, what amount must be deposited annually to reach your goal?

Amount needed at the time of retirement = 15000*(1-(1+9%)^-12)/9%

Amount needed at the time of retirement = $ 107410.88

Amount must be deposited annually = Amount needed at the time of retirement / (((1+r)^n-1)/r)

Amount must be deposited annually = 107410.88/(((1+9%)^30-1)/9%)

Amount must be deposited annually = $ 788

b) Suppose you just inherited a large sum of money. Rather than making equal annual payments, you decide to make one lump sum payment on your 36th birthday to cover your retirement needs. What amount do you need to deposit?

Amount needed at the time of retirement = 15000*(1-(1+9%)^-12)/9%

Amount needed at the time of retirement = $ 107410.88

Amount must be deposited = Amount needed at the time of retirement / ((1+r)^n)

Amount must be deposited   = 107410.88/((1+9%)^30)

Amount must be deposited   = $ 8095.68

c) Suppose your employer will contribute $250 into the account every year. In addition, you expect $10,000 distribution from a family trust fund on your 55th birthday, which you will also put into the retirement account. What amount do you need to deposit annually now to meet your retirement goal?

Amount needed at the time of retirement = 15000*(1-(1+9%)^-12)/9%

Amount needed at the time of retirement = $ 107410.88

Amount available from employer contribution at retirement = 250*(((1+9%)^30-1)/9%)

Amount available from employer contribution at retirement   = $ 34076.88

Amount available from family trust fund at retirement = 10000*(1+9%)^10

Amount available from family trust fund at retirement = $ 23673.64

Additional amount required at the time of retirement = 107410.88 - 34076.88 - 23673.64

Additional amount required at the time of retirement = $ 49660.36

Amount must be deposited annually =Additional Amount needed at the time of retirement / (((1+r)^n-1)/r)

Amount must be deposited annually = 49660.36/(((1+9%)^30-1)/9%)

Amount must be deposited annually = $ 364.33

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