To find the maximum amount you should pay for this investment, we need to calculate the present value of an annuity. The formula for the present value of an annuity is:

$PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)$

where:

• $P$ is the payment per period ($2114),
• $r$ is the monthly interest rate (annual rate of 10% divided by 12 months),
• $n$ is the total number of payments (10 years × 12 months).

Step 1: Determine $r$

The monthly interest rate is: $r = \frac{10\%}{12} = \frac{0.10}{12} = 0.0083333$

Step 2: Determine $n$

The total number of payments over 10 years is: $n = 10 \times 12 = 120$

Step 3: Calculate the present value (PV)

Now, we plug the values into the formula: $PV = 2114 \times \left( \frac{1 - (1 + 0.0083333)^{-120}}{0.0083333} \right)$

Calculating this step-by-step:

1. $1 + r = 1 + 0.0083333 = 1.0083333$
2. $(1 + r)^{-120} = 1.0083333^{-120} \approx 0.3638$
3. $1 - 0.3638 = 0.6362$
4. $\frac{0.6362}{0.0083333} \approx 76.34$
5. $PV = 2114 \times 76.34 \approx 161,360.76$

Thus, the maximum amount you should pay for this investment is $161,360.76.

Would you like a more detailed explanation, or do you have any other questions?

Related Questions:

1. How would the present value change if the cash flow occurred at the beginning of each month?
2. What happens to the present value if the required rate of return is increased to 12%?
3. How does compounding frequency affect the present value of an investment?
4. What if the investment period was reduced to 5 years? How would it impact the maximum price?
5. How would inflation affect the future cash flows of such an investment?

Tip:

When calculating the present value of an annuity, remember that as the interest rate increases, the present value decreases, since future cash flows are discounted more heavily.