Plan to save $5000 per year for retirement with first investment made 1 year from now.
Plan to earn 10% per year on investments.
Plan to retire in 43 years, immediately after making last $5000 investment.
a) if, instead, decide to withdraw $300,000 per year in retirement, with first withdrawal one year after retiring, how many years will it take until you exhaust your savings?
b)If you only save $1000 per year, but want to retire with $1 million in your investment account, how high of a return do you need to earn on your investments?
Thank you for helping me.
a) To find out how many years it will take until your savings are exhausted when you withdraw $300,000 per year in retirement, you need to calculate the total savings accumulated until retirement and then divide it by the yearly withdrawal amount.
The total savings accumulated would be the sum of all the annual contributions and the returns earned on these contributions over the 43 years.
Given:
- Annual contribution: $5000
- Return on investments: 10%
- Retirement period: 43 years
- Yearly withdrawal in retirement: $300,000
First, let's calculate the total savings accumulated until retirement:
1. Calculate the future value of each annual contribution using compound interest formula:
FV = PV * (1 + r)^n
Where:
PV = Present Value or annual contribution ($5000)
r = Annual interest rate (10% or 0.10)
n = Number of years until retirement (43)
Calculate FV for each year and sum them up:
FV_year1 = $5000 * (1 + 0.10)^43
FV_year2 = $5000 * (1 + 0.10)^42
FV_year3 = $5000 * (1 + 0.10)^41
...
FV_year43 = $5000 * (1 + 0.10)^1
Total savings accumulated until retirement = FV_year1 + FV_year2 + FV_year3 + ... + FV_year43
2. Once you have the total savings accumulated until retirement, divide it by the yearly withdrawal amount ($300,000) to find out the number of years it will sustain your retirement lifestyle.
b) To calculate the required return on investments needed to retire with $1 million in your investment account while saving only $1000 per year, you need to use the compound interest formula in reverse.
Given:
- Annual contribution: $1000
- Desired retirement savings: $1,000,000
- Years until retirement: Not mentioned
To calculate the required return on investments, you can rearrange the compound interest formula to solve for the interest rate (r):
FV = PV * (1 + r)^n
Where:
FV = Future Value or desired retirement savings ($1,000,000)
PV = Present Value or annual contribution ($1000)
n = Number of years until retirement
Rearranging the formula, we get:
(1 + r)^n = FV / PV
Taking the nth root of both sides:
1 + r = (FV / PV)^(1/n)
Now, solve for r:
r = (FV / PV)^(1/n) - 1
Plug in the given values to calculate the required return on investments.