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Thread: Constant percentage of annual salary: Your father has just turned 50 (t = 0)...

  1. #1

    Constant percentage of annual salary: Your father has just turned 50 (t = 0)...

    Hello, this is my first post. I need to solve some problems for my class, and I got stuck with this one.

    The problem (this is a translation):

    Your father has just turned 50 (t = 0) and wants to retire in 15 years (t = 15). He thinks he will live 25 years after retirement, until he is 90 years old. He wants an annual amount indexed to the cost of inflation that will give him a purchasing power at age 65 equivalent to $ 50,000 today (the amount of the benefit will therefore vary each year). His retirement benefits will start on his retirement day in 15 years (t = 15) and he will receive a total of 25 indexed benefits (from t = 15 to t = 39). Over the next 40 years, inflation will be 3% per year. Your father currently has savings of $ 300,000 and expects to earn 8% per year on his investments over the next 40 years. He would also like to give you $ 25,000 when he turns 90.


    a) How much should he save over the next 15 years (with equal deposits made at the beginning of the year, so from t = 0 to t = 14) to reach his retirement goals (ie what is the deposit amount annual)?

    I calculated the value of $ 50,000 in 15 years, with an inflation rate of 3%. Which gives me :
    FV15 = 50000(1,03)15
    FV15 = 77898,37$

    Then, I used this formula : PV0 (at t=15) = A1/(r-g) x [1 - (1+g)/(1+r)n] to find the PV (t=15) of the annuity with constant growth (77898,37$)
    Which gave me :
    PV0 = (77898,37/0,08-0,03)x[1-[(1+0,03)/(1+0,08)]25]
    PV0 = 1081651,48$

    Then, I updated the value of 25000$, to have its PV at t = 15
    25000/(1,08)25 = 3650,45$

    Then I added those numbers to have the amount he needs to have at t=15 --> 1081651,48 + 3650,45 = 1 085301,93$

    I capitalized the $ 300,000 to have its value at t = 15. And I subtracted this amount from the previous sum.

    300000(1,08)15= 951650,73$
    1 085301,93 - 951650,73 = 133 651,20$ --> so this is the amount he needs to have at t = 15. (FV)

    Then, I calculated the PMT with my calculator : [FV = 133 651,20] ; [N = 15] ; [I = 8] ; [PV = 0] ; [PMT = 4922,31]

    So he needs to save 4922,31$ every year to reach his retirement goals.



    I spent so much time trying to find a solution that I do not even know if I did the math. Which prevents me from solving the next exercise.

    (b) Pension contribution amounts are generally expressed as a percentage of annual salary, which means that the amount of contributions varies each year. If your father is currently earning $ 75,000 (at t = 0) and his salary will increase with inflation each year, what is the constant percentage of his annual salary that your father should save each year (from t = 0 to t = 14) to reach your retirement goals?

    So here I just do not know which formula to apply, or what is the logic behind this problem. It would be really nice if someone could help me! thank you in advance

  2. #2
    Quote Originally Posted by Denis View Post
    Agree with your calculations.
    In Bank statement format, the picture looks like this:
    (omitted the pennies!)
    Code:
    AGE TRANSACTION INTEREST(8%) BALANCE
    50                           300,000
    51    4,922       24,000     328,922
    52    4,922       26,314     360,158
    .....
    65    4,922       80,028   1,085,302
    66  -77,898       86,824   1,094,228
    67  -80,235       87,538   1,101,531
    ....
    75 -101,640       87,035   1,073,328
    ....
    89 -153,739       23,964     169,769
    90 -158,351       13,582      25,000 : your gift!
    Good luck!

    Thank you very much!! So for question (b) I know I have to use the PMT found at (a) = 4922$ but I don't really know what formula to use. I tried with the same one used the same one that I used in (a) = A1/(r-g) x [1 - (1+g)/(1+r)n] but it's not right.

    Would you have any idea of what I have to do? Thank you very much!


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