Sheila deposits 5,900 annually into Ira earning 10 percent interest compound annually. If she invests $491.67 monthly and the investment also changed to monthly compounding , how much would she have after in 20 years 

The two scenarios you describe differ in terms of deposit frequency and interest compounding, so I'll go through each step.

### 1. **Scenario 1: Annual Deposit with Annual Compounding**
In the first case, Sheila deposits $5,900 annually with an annual interest rate of 10%, compounded annually. This follows the formula for future value of an annuity:

\[
FV = P \times \frac{{(1 + r)^n - 1}}{r}
\]

Where:
- $ P = 5900 $ (annual deposit)
- $ r = 0.10 $ (annual interest rate)
- $ n = 20 $ (number of years)

### 2. **Scenario 2: Monthly Deposit with Monthly Compounding**
In this case, Sheila deposits $491.67 monthly (which sums up to $5,900 annually) with a monthly interest rate of $ \frac{10\%}{12} $. The future value for a monthly deposit compounded monthly is given by:

\[
FV = P \times \frac{{(1 + \frac{r}{12})^{12 \times n} - 1}}{\frac{r}{12}}
\]

Where:
- $ P = 491.67 $ (monthly deposit)
- $ r = 0.10 $ (annual interest rate)
- $ n = 20 $ (number of years)

I’ll now calculate the future value for each scenario.Here are the results after 20 years:

1. **Annual Deposit with Annual Compounding**: Sheila would accumulate **$337,922.50**.
2. **Monthly Deposit with Monthly Compounding**: Sheila would accumulate **$373,358.88**.

The monthly deposit with monthly compounding results in a higher future value due to more frequent contributions and compounding.

Would you like more details on these calculations or have any other questions?

### Related Questions:
1. What happens if the interest rate changes after a few years?
2. How would the final amount differ if the compounding was done quarterly instead of monthly?
3. What if Sheila increases her monthly deposit by a certain percentage each year?
4. How does the total future value compare if Sheila deposits annually with monthly compounding?
5. What would the future value be if Sheila deposits for only 15 years?

### Tip:
Always maximize the frequency of contributions and compounding periods to take better advantage of compound interest.

Sheila deposits 5,900 annually into Ira earning 10 percent interest compound annually. If she invests $491.67 monthly and the investment also changed to monthly compounding, how much would she have after 20 years?

Learn how to calculate the future value of Sheila's IRA with annual deposits of $5,900 compounded annually and monthly deposits of $491.67 with monthly compounding over 20 years. This problem covers key concepts like compound interest, annuities, and the time value of money.

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