Two oil wells are for sale. The first will yield payments of $11,700 at the end of each of the next 13 years, while the second will yield $6,500 at the end of each of the next 27 years. Interest rates are assumed to hold steady at 8.1% per year over the next 27 years. Which has the higher present value?

the first oil wellthe second oil well    they are the samecannot be determined

To determine which oil well has the higher present value (PV), we use the formula for the present value of an annuity. The formula is:

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

Where:
- $P$ is the payment per period,
- $r$ is the interest rate per period,
- $n$ is the number of periods.

### 1. Present Value of the First Oil Well:
- Payment ($P_1$) = $11,700
- Interest rate ($r$) = 8.1% = 0.081
- Number of periods ($n_1$) = 13

\[
PV_1 = 11,700 \times \frac{1 - (1 + 0.081)^{-13}}{0.081}
\]

### 2. Present Value of the Second Oil Well:
- Payment ($P_2$) = $6,500
- Interest rate ($r$) = 8.1% = 0.081
- Number of periods ($n_2$) = 27

\[
PV_2 = 6,500 \times \frac{1 - (1 + 0.081)^{-27}}{0.081}
\]

Let me calculate both values to compare the present values of the two oil wells.The present value (PV) of the first oil well is approximately **$91,967.71**, while the present value of the second oil well is approximately **$70,448.98**. 

Thus, the **first oil well** has the higher present value.

Would you like more details or have any questions?

Here are five related questions for further exploration:
1. How does the interest rate impact the present value of the oil wells?
2. What happens to the present values if the interest rate changes to 10%?
3. How does increasing the number of years affect the present value?
4. Could an alternative investment yield a better present value than either oil well?
5. How can we compare present values when payments occur at different intervals (monthly vs annually)?

**Tip:** The longer the payment period and the smaller the annual payment, the lower the present value for the same interest rate.

Two oil wells are for sale. The first will yield payments of $11,700 at the end of each of the next 13 years, while the second will yield $6,500 at the end of each of the next 27 years. Interest rates are assumed to hold steady at 8.1% per year over the next 27 years. Which has the higher present value? The first oil well, the second oil well, they are the same, or cannot be determined.

Explore how to calculate the present value of two oil wells with different annual payments and time periods. Using the annuity formula and a fixed interest rate of 8.1%, we determine which oil well has the higher present value. Suitable for finance and business students.

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