Your grandmother left you an inheritance that pays $**550** at the end of each year for a total of **15** consecutive years.
However, because of your young age, the payments will not begin until the end of **4** years. If the interest rate is **9.00**%, what is the equivalent value of your inheritance today?

To determine the equivalent value of your inheritance today, we need to calculate the present value (PV) of the series of future payments. The payments are deferred, starting after 4 years, and they last for 15 years with an interest rate of 9%.

### Step 1: Present Value of Annuity Formula
We’ll use the present value of an annuity formula:

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

Where:
- $ P = 550 $ is the payment at the end of each year.
- $ r = 9\% = 0.09 $ is the annual interest rate.
- $ n = 15 $ years is the duration of payments.

This formula will give the present value of the annuity at the beginning of year 5, just before the payments start.

### Step 2: Discount the Annuity to Today
Since payments begin after 4 years, we need to discount the present value we calculate for the annuity back to today. The discount factor is $ (1 + r)^t $, where $ t = 4 $ years. So, we’ll discount the result from Step 1 by $ (1 + 0.09)^4 $.

Let’s now compute these values.The equivalent value of your inheritance today, given the deferred payments and interest rate, is approximately **$3,140.72**.

Would you like more details on any step? Here are some related questions to consider:

1. What is the present value of a deferred annuity in general terms?
2. How does the interest rate affect the present value of future payments?
3. What would the present value be if the interest rate was higher or lower?
4. How does the deferred period (4 years in this case) impact the present value?
5. How would the present value change if the payment period (15 years) was extended or shortened?

**Tip:** The longer you wait for payments to start, the more the present value decreases due to the time value of money.

Your grandmother left you an inheritance that pays $550 at the end of each year for a total of 15 consecutive years. However, because of your young age, the payments will not begin until the end of 4 years. If the interest rate is 9.00%, what is the equivalent value of your inheritance today?

Learn how to calculate the present value of a deferred annuity with an annual payment of $550 for 15 years, starting after 4 years at an interest rate of 9%. This problem explains key finance concepts like the time value of money, discounting future payments, and calculating annuity present value.

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