168k views
4 votes
Buying a "vacation timeshare" means buying the right to use a vacation property for a fixed period each year. Suppose that you pay $900 for a vacation timeshare and receive a "money-back guarantee" that at any time the company will buy back your timeshare, or if not, give you a $1800 bond. The deception, however, is that the bond is not redeemable for 45 years. Find the real value of the "guarantee" - that is, find the present value of $1800 in 45 years

User Knyri
by
8.4k points

1 Answer

2 votes

Final answer:

The student is inquiring about the present value of a future sum, requiring an understanding of the principles of financial mathematics, specifically present discounted value. Without the interest rate, it is not possible to calculate the exact present value of the bond. If an annual interest rate was provided, we could apply the present value formula to find the value of the bond today.

Step-by-step explanation:

The student is asking about the concept of present discounted value, which is a financial mathematics concept used to calculate the current worth of a future sum of money given a specific interest rate. To find the present value of an $1800 bond redeemable in 45 years, we would need to know the interest rate to be used for discounting. However, the question does not provide an interest rate. If we were given an interest rate, say 5%, the formula we would use is PV = FV / (1 + i)^n, where PV is the present value, FV is the future value ($1800), i is the interest rate (as a decimal), and n is the number of periods (45 years).

Assuming an interest rate of 5%, let's calculate the present value:

PV = $1800 / (1 + 0.05)^45
PV = $1800 / 7.04058
PV = approximately $255.69

Therefore, the present value of the $1800 bond, redeemable in 45 years at a 5% interest rate, would be approximately $255.69 today. This highlights the effect of time value of money and interest rate risk on investments.

User Changhoon
by
7.4k points