To find the present value (PV) of the $1200 bond that is redeemable in 45 years at a 4% interest rate compounded annually, we can use the formula for present value:

$PV = \frac{FV}{(1 + r)^n}$

where:

• $FV$ is the future value ($1200),
• $r$ is the annual interest rate (4% or 0.04),
• $n$ is the number of years until redemption (45 years).

Now, we can substitute the values into the formula:

$PV = \frac{1200}{(1 + 0.04)^{45}}$

Calculating $(1 + 0.04)^{45}$:

$(1.04)^{45} \approx 7.108$

Now, substitute this value back into the present value formula:

$PV = \frac{1200}{7.108} \approx 169.05$

Thus, the present value of the $1200 bond in 45 years at a 4% interest rate is approximately $169.05.

Summary:

The real value of the "guarantee" is $169.05.

Do you want further details or have any questions? Here are some related questions you might consider:

1. How does changing the interest rate affect the present value?
2. What would be the present value if the bond were redeemable in 30 years instead of 45?
3. How does inflation impact the value of a future payment?
4. What are the advantages and disadvantages of investing in a timeshare?
5. Can you explain the difference between present value and future value?

Tip: Understanding the impact of interest rates and time on investments is crucial in making informed financial decisions.