Roth vs Traditional IRA Comparison Calculator

What is an IRA?

An Individual Retirement Account (IRA) is a savings plan that offers tax advantages for individuals to set aside money for retirement. There are two main types of IRAs: Roth and Traditional. Each has its own tax benefits and rules for contributions and withdrawals.

Formula for Calculating IRA Savings

The formula to calculate the future value of your IRA 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 ($C$): $$C=\mathrm{\$}6,000$$
3. Apply the rate of return ($r$) and number of years ($n$): $$r=7\mathrm{\%}$$ $$n=30\text{ years}$$
4. Calculate the future value ($FV$) using the formula: $$FV=PV+\sum _{i=1}^{30}(6,000\times (1+0.07{)}^i)$$ $$FV=\mathrm{\$}10,000+\mathrm{\$}6,000\times \left(\frac{(1+0.07{)}^{30}-1}{0.07}\right)$$ $$FV=\mathrm{\$}10,000+\mathrm{\$}6,000\times 94.461$$ $$FV=\mathrm{\$}10,000+\mathrm{\$}566,766$$ $$FV=\mathrm{\$}576,766$$

Example Calculation

Let's calculate the future value of an IRA for an individual with the following details:

• Current Savings ($PV$): $10,000
• Annual Contribution: $6,000
• Rate of Return ($r$): 7%
• Years Until Retirement ($n$): 30 years

Using the formula, we get:

1. Initial savings: $PV=\mathrm{\$}10,000$
2. Annual contributions: $C=\mathrm{\$}6,000$
3. Rate of return: $r=7\mathrm{\%}$
4. Number of years: $n=30$
5. Future value: $$FV=10,000+\sum _{i=1}^{30}(6,000\times (1+0.07{)}^i)$$ $$FV=\mathrm{\$}10,000+\mathrm{\$}6,000\times \left(\frac{(1+0.07{)}^{30}-1}{0.07}\right)$$ $$FV=\mathrm{\$}10,000+\mathrm{\$}6,000\times 94.461$$ $$FV=\mathrm{\$}10,000+\mathrm{\$}566,766$$ $$FV=\mathrm{\$}576,766$$

Visual Representation

The green portion of the bar represents the calculated future value ($576,766) relative to the maximum possible value.