You just received your tax refund of $5,100.00 and you invest it in an annuity that pays 5.3%, compounded monthly. If you withdraw the money at the beginning of each month for the next 1 year(s). How much will each payment be?

The payment would be

To find the payment amount for an annuity where a lump sum is invested and monthly withdrawals are made over a period of time, we use the **formula for the present value of an annuity**:

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

Where:
- $PV$ is the present value (initial amount, $5,100 in this case),
- $P$ is the monthly payment (what we want to find),
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the number of months (12 for 1 year).

We can rearrange this formula to solve for $P$:

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

### Given values:
- $PV = 5100$
- Annual interest rate = 5.3%, so monthly interest rate $r = \frac{5.3\%}{12} = 0.0044167$
- Number of months $n = 12$

Let me now calculate the payment amount using these values.The monthly payment for the annuity, if you withdraw the money at the beginning of each month for the next 1 year, would be approximately **$437.30**.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does compounding affect the growth of your investment over time?
2. What would happen if the interest rate were higher or lower?
3. How would the payment change if the investment duration were longer than 1 year?
4. What is the total interest earned over the 1-year period?
5. How do monthly withdrawals affect the balance of the annuity?

**Tip:** The more frequently interest is compounded, the more your investment can grow due to the interest-on-interest effect.

You just received your tax refund of $5,100.00 and you invest it in an annuity that pays 5.3%, compounded monthly. If you withdraw the money at the beginning of each month for the next 1 year(s). How much will each payment be?

Learn how to calculate monthly withdrawals from a $5,100 annuity invested at 5.3% interest, compounded monthly, over a 1-year period. This problem involves key financial concepts such as annuities, present value, and compound interest. Suitable for students in Grades 10-12.

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