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To find the present value of a series of monthly deposits compounded monthly, we use the present value of an ordinary annuity formula. Given the following details:

- Monthly deposit ($ PMT $) = $150
- Annual interest rate ($ r $) = 4.5% (or 0.045)
- Compounded monthly, so the monthly interest rate ($ i $) = $ \frac{0.045}{12} $
- Number of years ($ t $) = 14
- Number of monthly deposits ($ n $) = 14 years × 12 months/year = 168

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

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

Let's calculate it step by step.

1. Monthly interest rate $ i $ = $ \frac{0.045}{12} \approx 0.00375 $
2. Total number of payments $ n $ = 168
3. Calculate $ (1 + i)^{-n} $
4. Substitute into the formula to find $ PV $. 

Let's perform this calculation.The present discounted value of the deposits is approximately **$18,671.21**.

Would you like more details or have any questions about this calculation?

Here are some related questions that might interest you:
1. How does changing the interest rate affect the present value of an annuity?
2. What if the deposits were made at the beginning of each month instead of the end?
3. How is the present value different from the future value of an annuity?
4. What if the interest was compounded annually instead of monthly?
5. How does the length of time affect the present value of monthly deposits?

**Tip:** The present value of an annuity is lower than the total sum of payments because the money has the potential to earn interest over time.

What is the present discounted value of deposits of $150.00 made at the end of each month for 14 years if the interest is 4.5%, compounded monthly?

Find the present discounted value of $150 monthly deposits made over 14 years, with an interest rate of 4.5% compounded monthly. This calculation uses the Present Value of an Ordinary Annuity formula to solve the problem. Ideal for finance and advanced math students.

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