# Find Constant % of Annual Salary to Reach Retirement Goal

• MHB
• MariaAM
In summary, the problem involves a father who wants to retire in 15 years, live for 25 years after retirement, and receive an annual amount indexed to inflation that is equivalent to $50,000 today. He currently has savings of$300,000 and expects to earn 8% per year on his investments. To reach his retirement goals, he needs to save $4,922.31 every year for the next 15 years. Additionally, to reach his retirement goals, he should save a constant percentage of his annual salary, which will increase with inflation each year. MariaAM 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 :D

The whole episode in Bank statement format:
(pennies dropped!)
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!

MariaAM said:
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.

## 2. What is the recommended constant % of annual salary for retirement?

The recommended constant % of annual salary for retirement may vary depending on individual financial goals and circumstances. However, a common recommendation is to save at least 10-15% of your annual salary for retirement.

## 3. Can I adjust the constant % of my annual salary for retirement as I get closer to retirement age?

Yes, it is recommended to adjust the constant % of your annual salary for retirement as you get closer to retirement age. As you approach retirement, you may want to increase your savings to ensure you have enough funds for your desired retirement income.

## 4. What happens if I don't save the recommended constant % of my annual salary for retirement?

If you do not save the recommended constant % of your annual salary for retirement, you may not have enough funds to support your desired retirement lifestyle. This could result in having to rely on other sources of income or reducing your retirement expectations.

## 5. Are there any tools or resources to help me determine the constant % of my annual salary for retirement?

Yes, there are various retirement calculators and financial planning resources available that can help you determine the constant % of your annual salary needed for retirement. It is also recommended to seek the advice of a financial advisor for personalized guidance.