## Roth IRA Calculator

A Roth IRA can be defined as a retirement savings account or a tax-advantaged account, which shall allow one to withdraw the amount from the savings account as tax-free. The below calculator will help you find the total amount.

#### Roth IRA Calculator

O x (1+i)^{Fxn} + I x [((1+i)^{Fxn} – 1)x (1+i) / i ]

- O is the amount already deposited
- I is the periodical fixed amount invested at regular intervals
- i is the rate of interest
- F is the frequency of interest being paid
- n is the the number of periods for which savings shall be made.

### About Roth IRA Calculator

The formula for calculating Roth IRA is per below:

**Periodical Roth IRA **

**O * (1+i)**

^{F * n}+ I * [(1+i)^{F * n}– 1 / i ]**Investment is made at the beginning of the period**

**O * (1+i)**

^{F * n}+ I * [((1+i)^{F * n}– 1)* (1+i) / i ]Wherein,

- O is the starting account balance
- I is the periodical fixed amount invested at regular intervals
- i is the rate of interest
- F is the frequency of interest is paid
- n is the number of periods for which Roth IRA shall be made.

IRA stands for an investment retirement plan and is a special type of account wherein individuals pay taxes on the money which is going into this account, and it will be tax-free for all its future withdrawals. These kinds of accounts can be used when one feels that taxes at the time of retirement will be higher, and it’s better off paying taxes at the moment. The contribution to Roth IRA account can be made from a number of sources, which include regular contribution, transfer, spousal IRA contributions, etc.

These can only be made in cash and not in gold or securities. Further, the IRA account limits the amount that can be deposited in any type of IRA account, and a variety of options exist within it that is mutual funds, bonds, stock, etc. Roth IRA calculator will help the individual to calculate the amount that he would be having at the time of retirement, which again, as stated earlier, will be a tax-free amount.

### How to Calculate using Roth IRA Calculator?

One needs to follow the below steps in order to calculate the maturity amount.

**Step #1: **Determine the initial balance of the account, if any, and also, there will be a fixed periodical amount that will be invested in the Roth IRA.

**Step #2: **Figure out the rate of interest that would be earned on the Roth IRA.

**Step #3: **Now, determine the duration which is left from current age till the age of retirement.

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**Step #4: **Divide the rate of interest by the number of periods the interest or the Roth IRA income is paid. For example, if the rate paid is 5% and it compounds semi-annually, then the rate of interest would be 5%/2, which is 2.50%.

**Step #5: **Determine whether the contributions are made at the start of the period or at the end of the period.

**Step #6: **Now, use the formula accordingly that was discussed above for calculating the maturity value of the Roth IRA, which is made at regular intervals.

**Step #7: **The resultant figure will be the maturity amount that would include the Roth IRA income plus the amount contributed.

**Step #8: **There would be no tax liability at the time of retirement since the contributions that are made are after-tax, and no deductions are taken for the amount that is contributed.

### Example #1

Mr. Y is a US resident for almost 15 years now and has been working there. He is now considering a retirement plan for himself, and he believes that in future, the tax rates will be higher when he reaches retirement age and hence, he decides to invest in a Roth IRA plan wherein he wants to deposit 20% of his pretax income of $12,500 that he earns annually. The current tax rate is 20%. He is considering investing for 25 years, and the return that he expects from this Roth IRA account is 5.50%, which compounds annually.

Based on the given information, you are required to calculate the amount that would be accumulated at the time of maturity.

**Solution:**

We are given the below details:

- O = NIL
- I = Fixed amount deposited periodically which would be $12,500 x 20% x (1 – 0.20) which is $2,000
- i = Rate of interest, which is 5.50% and is compounded annually
- F = Frequency which is annually here, hence it will be 1
- n = number of years the Roth IRA proposed to be made will 25 years.

Now, we can use the below formula to calculate the maturity amount.

**IRA = O * (1+i)**

^{F * n}+ I * [((1+i)^{F * n}– 1)* (1+i) / i ]- = 0 * ( 1 + 5.50% )
^{1 * 25}+ $ 2,000 * [(1+5.50%)^{1 * 25}– 1 * (1+5.50%) / 5.50%] **= $ 107,931.96**

At the time of retirement when he withdraws the amount, he will not be liable for any tax, since the contributions are made tax free and no deduction is taken for contributions that are made.

### Example #2

Mrs. Ak is a well educated and independent person; she has been maintaining her finance quite well. At the age of 18, her dad started making contributions to Roth IRA account, and now when she is 30 years old, she has accumulated $25,677 in her account. Now she plans to contribute $1,250 every year post-tax amount to the same account to accumulate a good amount of wealth as tax-free when she retires at the age of 65. She deposits the amount at the end of the year. The IRA account pays 4.75% compounded annually.

Based on the given information, you are required to calculate the maturity amount.

**Solution:**

We are given the below details:

** **

- O = $25,677
- I = Fixed amount deposited periodically, which is $1,250
- i = Rate of interest, which is 4.75% and is compounded annually
- F = Frequency which is annually here, hence it will be 1
- n = number of years the Roth IRA proposed to be made will be different of retirement age less current age (65 – 30), which is 35 years.

Now, we can use the below formula to calculate the maturity amount.

**IRA = O * (1+i)**

^{F * n}+ I * [(1+i)^{F * n}– 1 / i ]- = $ 25,667 * ( 1 + 4.75% )
^{1 * 35}+ $ 1,250 * [(1+4.75%)^{1 * 35}– 1 / 4.75%] **= $ 237,520.31**

At the time of retirement, she will not be liable for any tax, and hence the amount that will be received will be $237,520.31

### Conclusion

As discussed, a Roth IRA account can be used by the individuals to deposit the tax-paid amount and without taking any deductions for their contributions and receiving the tax-free amount at the time of withdrawals. However, individuals use this account to accumulate wealth as tax-free, and therefore the government has set up a limit that one can deposit in this account; one needs to be aware of that.

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