I posted this under business the first time and got no answer so since its more mathematical here it is again:
I can only put away $1,000 a year toward retirement. I am 22 and plan on retiring at 65 and earning 6%. How much will I have at retirement?
Not positive the answer I got is correct..my answer is $464,215.00
To calculate the future value of your retirement savings, you can use the formula for compound interest:
FV = PV * (1 + r)^n
Where:
FV = Future Value
PV = Present Value (initial investment or contribution)
r = Annual interest rate (in decimal form)
n = Number of compounding periods
In your case, the present value (PV) is $1,000 per year, the annual interest rate (r) is 6% or 0.06, and the number of years (n) is 65 - 22 = 43.
First, let's calculate the future value for the annual contributions:
FV_contributions = $1,000 * ((1 + 0.06)^43 - 1) / 0.06
The formula (1 + 0.06)^43 - 1 calculates the future value of a regular payment.
FV_contributions = $1,000 * (1.06^43 - 1) / 0.06
Using a calculator, the value of (1.06^43 - 1) / 0.06 is approximately 89.3086277.
FV_contributions = $1,000 * 89.3086277 ≈ $89,309
The future value of your contributions will be approximately $89,309.
Next, let's calculate the future value for the compound interest on those contributions:
FV_interest = $1,000 * (1 + 0.06)^43
Using a calculator, the value of (1 + 0.06)^43 is approximately 6.82462165.
FV_interest = $1,000 * 6.82462165 ≈ $6,825
The future value of compound interest on your contributions will be approximately $6,825.
Finally, add the future value of contributions and the future value of compound interest:
Total future value = FV_contributions + FV_interest
= $89,309 + $6,825
= $96,134
Therefore, based on your calculations, you would have approximately $96,134 at retirement, which is different from your initial answer of $464,215.00.