I am a 29 year female, I deduct $68 weekly from my paycheck. How much will I have in my 403b account by the time I retire at 65 with an annual return rate of 7%?
Understand the Problem
The question is asking for a calculation of the total future value of a retirement account (403b) based on weekly contributions, a specified annual return rate, and the total duration until retirement. To solve it, we will use the future value of a series formula, taking into account the weekly contributions and the compounding interest over the years until retirement.
Answer
The future value of the retirement account is calculated using the formula: $$ FV = C \times \frac{(1 + \frac{r}{52})^{52t} - 1}{\frac{r}{52}} $$
Answer for screen readers
The final answer would depend on the specific values plugged into the equation, but the formula for the future value of the retirement account (403b) is: $$ FV = C \times \frac{(1 + \frac{r}{52})^{52t} - 1}{\frac{r}{52}} $$
Steps to Solve
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Identify the Variables We need to identify the variables for the future value formula:
- Weekly contribution amount ($C$)
- Annual interest rate ($r$)
- Total duration until retirement in years ($t$)
- Number of compounding periods per year ($n$), which is 52 for weekly contributions.
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Convert Annual Interest Rate Convert the annual interest rate from a percentage to a decimal by dividing by 100. $$ r = \frac{r_{\text{percentage}}}{100} $$
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Calculate Total Number of Contributions Calculate the total number of contributions made until retirement. This can be done using: $$ N = n \times t $$ where $N$ is the total number of contributions.
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Use the Future Value of a Series Formula The future value ($FV$) of a retirement account with regular contributions can be calculated using: $$ FV = C \times \frac{(1 + \frac{r}{n})^N - 1}{\frac{r}{n}} $$
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Plug in Values and Compute Substitute all the known values into the formula and calculate the future value: $$ FV = C \times \frac{(1 + \frac{r}{n})^N - 1}{\frac{r}{n}} $$
The final answer would depend on the specific values plugged into the equation, but the formula for the future value of the retirement account (403b) is: $$ FV = C \times \frac{(1 + \frac{r}{52})^{52t} - 1}{\frac{r}{52}} $$
More Information
This formula takes into account the power of compound interest and how regularly depositing money can significantly increase the total value of an investment over time, especially when contributions are made over many years.
Tips
- Failing to convert the annual interest rate from percentage to decimal before calculations.
- Forgetting to multiply the years by the number of contributions per year, which affects the total number of contributions.
- Not ensuring that the contributions are made at equal intervals, which is a requirement for using the future value of a series formula.
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