Savings Calculator

What is a 401k Retirement Plan?

A 401k retirement plan is a savings plan sponsored by an employer that allows employees to save and invest a portion of their paycheck before taxes are taken out. Taxes aren't paid until the money is withdrawn from the account.

Formula for Calculating 401k Savings

The formula to calculate the future value of your 401k savings is:

$$FV=PV+\sum _{i=1}^n(C\times (1+r{)}^i)$$

Where:

• $FV$ = Future Value (total savings)
• $PV$ = Present Value (current savings)
• $C$ = Annual Contribution
• $r$ = Rate of Return
• $n$ = Number of Years

Step-by-Step Calculation

1. Determine the initial savings ($PV$): $$PV=\mathrm{\$}10,000$$
2. Calculate the annual contributions ($C$): $$C=\text{Annual Employee Contribution}+\text{Annual Employer Contribution}$$ $$C=\mathrm{\$}5,000+\mathrm{\$}3,000=\mathrm{\$}8,000$$
3. Apply the rate of return ($r$) and number of years ($n$): $$r=5\mathrm{\%}$$ $$n=20\text{ years}$$
4. Calculate the future value ($FV$) using the formula: $$FV=PV+\sum _{i=1}^{20}(8,000\times (1+0.05{)}^i)$$

Example Calculation

Let's calculate the future value of a 401k plan for an individual with the following details:

• Current Savings ($PV$): $10,000
• Annual Employee Contribution: $5,000
• Annual Employer Contribution: $3,000
• Rate of Return ($r$): 5%
• Years Until Retirement ($n$): 20 years

Using the formula, we get:

1. Initial savings: $PV=\mathrm{\$}10,000$
2. Annual contributions: $C=\mathrm{\$}8,000$
3. Rate of return: $r=5\mathrm{\%}$
4. Number of years: $n=20$
5. Future value: $$FV=10,000+\sum _{i=1}^{20}(8,000\times (1+0.05{)}^i)$$ $$FV=\mathrm{\$}10,000+\mathrm{\$}8,000\times \left(\frac{(1+0.05{)}^{20}-1}{0.05}\right)$$ $$FV=\mathrm{\$}10,000+\mathrm{\$}8,000\times 33.066$$ $$FV=\mathrm{\$}10,000+\mathrm{\$}264,528$$ $$FV=\mathrm{\$}274,528$$

Visual Representation

The green portion of the bar represents the calculated future value ($274,528) relative to the maximum possible value.