**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 9% 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

We can solve this problem using the concept of the **present value of an annuity**. Since you want to ensure a monthly payment of $1,500 for 18 years, with an interest rate of 9% compounded monthly, the goal is to find the present value of these monthly payments.

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

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

Where:
- $PV$ is the present value (the amount of the life insurance policy).
- $P$ is the monthly payment (\$1,500).
- $r$ is the monthly interest rate (9% annual interest rate compounded monthly, so $r = \frac{0.09}{12}$).
- $n$ is the number of compounding periods per year (12 for monthly compounding).
- $t$ is the number of years (18 years).

Now, let’s calculate this step-by-step.

1. Monthly interest rate $r = \frac{0.09}{12} = 0.0075$.
2. Number of total payments over 18 years: $n \times t = 12 \times 18 = 216$.

Using these values in the formula, I’ll calculate the present value $PV$.The life insurance policy should be worth approximately **$160,180.28** in order to provide your child with a monthly payment of $1,500 for 18 years, assuming the money is invested at 9% interest compounded monthly.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How would the policy amount change if the interest rate were lower, say 6%?
2. What if you wanted the payments to last for 25 years instead of 18?
3. How does compounding frequency affect the required insurance amount?
4. How much would be needed if you increased the monthly payment to $2,000?
5. What is the effect of starting payments immediately rather than at the end of each month?

**Tip**: The longer the payment period, the more the compounding effect works in your favor, reducing the initial amount you need!

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 9% 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?

Learn how to calculate the necessary life insurance policy value to provide a monthly payment of $1,500 for 18 years. This financial math problem involves calculating the present value of an annuity with 9% interest compounded monthly. Step-by-step explanation provided.

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