After the birth of your first child, you decide to buy a life insurance policy for yourself but can't decide how much to buy. In the event of your untimely death, you estimate that the life insurance money can be invested in an account earning 6% interest compounded monthly. You would like your child to get a monthly payment of $1,500.00 for 18 years.

How much should your life insurance policy be worth in order to achieve your goal?
I should get a life insurance policy that is worth 

To find the value of the life insurance policy, we need to calculate the present value of an annuity because you're looking for a lump sum (the life insurance payout) that will provide monthly payments for 18 years.

Here's the breakdown:

- Monthly payment ($P$) = $1,500
- Interest rate = 6% annually, compounded monthly, which is 0.5% per month (i.e., $r = \frac{6\%}{12} = 0.005$)
- Duration = 18 years or 216 months (since 18 years * 12 months/year = 216 months)

The formula for the present value of an ordinary annuity is:

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

Where:
- $PV$ is the present value (the amount the life insurance policy should be worth),
- $P$ is the monthly payment ($1,500),
- $r$ is the monthly interest rate (0.005),
- $n$ is the total number of months (216).

Now let's calculate the present value.It seems there's an issue with running the calculation right now, but I can walk you through how to do it manually.

We have the values:
- $ P = 1500 $
- $ r = 0.005 $ (monthly interest rate)
- $ n = 216 $ months.

Plugging these into the formula:

\[
PV = 1500 \times \frac{1 - (1 + 0.005)^{-216}}{0.005}
\]

1. First, calculate $ (1 + 0.005)^{-216} $:
   \[
   (1.005)^{-216} \approx 0.352
   \]

2. Then calculate $ 1 - 0.352 = 0.648 $.

3. Now divide by $ 0.005 $:
   \[
   \frac{0.648}{0.005} = 129.6
   \]

4. Finally, multiply by 1500:
   \[
   PV = 1500 \times 129.6 = 194,400
   \]

So, the life insurance policy should be worth approximately **$194,400** to provide monthly payments of $1,500 for 18 years.

Would you like further clarification, or details on any part of the process?

### Follow-up questions:
1. What happens if the interest rate changes to 5%?
2. How would the result change if payments are for 25 years instead of 18?
3. How does the frequency of compounding affect the insurance value?
4. What formula is used if the interest is compounded continuously?
5. How can I calculate the future value of this annuity instead?

#### Tip:
Always ensure to account for inflation when planning for long-term financial goals, as it impacts the value of money over time.

After the birth of your first child, you decide to buy a life insurance policy for yourself but can't decide how much to buy. In the event of your untimely death, you estimate that the life insurance money can be invested in an account earning 6% interest compounded monthly. You would like your child to get a monthly payment of $1,500.00 for 18 years. How much should your life insurance policy be worth in order to achieve your goal?

Learn how to determine the value of a life insurance policy that will provide monthly payments of $1,500 for 18 years, assuming a 6% interest rate compounded monthly. This financial mathematics problem uses the present value of annuity formula and compound interest calculations. Ideal for advanced high school or college students.

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