To determine the value of $X$ (the payment you will receive in 13 years), we need to use the concept of the present value of an investment. The present value of all future cash flows, discounted at the given rate of return, should equal the current value of the investment.

Given:

• Current value of the investment $PV = 97,030$
• Expected return $r = 6.15\%$ per year
• Payment in 2 years $C_1 = 68,000$
• Payment in 13 years $C_2 = X$

The present value of the cash flows is given by the formula: $PV = \frac{C_1}{(1 + r)^2} + \frac{C_2}{(1 + r)^{13}}$ Substituting the values: $97,030 = \frac{68,000}{(1 + 0.0615)^2} + \frac{X}{(1 + 0.0615)^{13}}$

We will now solve for $X$.

Step 1: Calculate the present value of $C_1 = 68,000$ discounted for 2 years.

$\frac{68,000}{(1 + 0.0615)^2} = \frac{68,000}{1.0615^2}$

Step 2: Subtract this value from the total present value of the investment to find the present value of $C_2 = X$.

$97,030 - \frac{68,000}{(1.0615)^2} = \frac{X}{(1.0615)^{13}}$

Step 3: Solve for $X$.

Let's compute it step by step.It seems there was an issue with processing the calculation. Let's try solving it manually:

Step 1: Calculate the present value of $C_1 = 68,000$ discounted for 2 years.

$\text{PV of } C_1 = \frac{68,000}{(1 + 0.0615)^2} \approx \frac{68,000}{1.1265} \approx 60,354.21$

Step 2: Subtract this from the total present value:

$97,030 - 60,354.21 = 36,675.79$

Step 3: Solve for $X$:

$\frac{X}{(1.0615)^{13}} = 36,675.79$ $X = 36,675.79 \times (1.0615)^{13} \approx 36,675.79 \times 2.1251 \approx 77,931.45$

Therefore, $X \approx 77,931.45$.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How does the discount rate affect the present value of future cash flows?
2. What would happen to $X$ if the expected return was higher or lower?
3. How is the present value concept used in comparing different investment options?
4. What is the relationship between present value and net present value (NPV)?
5. How would changing the time period of the cash flows affect the calculation?

Tip: When calculating present values, be mindful of the compounding frequency, as it significantly impacts the results.