Final answer:
The present value of a security with future payments can be calculated using a discount rate to find today's value. For payments of $1,100, $1,200, and $1,300 over the next three years at a 5% rate, the total present value is $3,260.14. If the discount rate increases, the present value of future payments would decrease.
Step-by-step explanation:
The present value of a security that pays $1,100 next year, $1,200 the year after that, and $1,300 the year after that at an interest rate of 5% can be calculated using the present value formula. This involves discounting each payment by the interest rate to find out what these payments are worth in today's dollar terms.
The formula for the present value (PV) of a future amount (FV) due in n years at an interest rate i is given by: PV = FV / (1 + i)^n. Applying this formula to each payment:
- Year 1: PV = $1,100 / (1 + 0.05)^1 = $1,047.62
- Year 2: PV = $1,200 / (1 + 0.05)^2 = $1,088.44
- Year 3: PV = $1,300 / (1 + 0.05)^3 = $1,124.08
The total present value is the sum of the present values of each payment: Total PV = $1,047.62 + $1,088.44 + $1,124.08 = $3,260.14.
If the interest rates rise, the present value would be lower because the future payments are discounted at a higher rate. This reflects the increased opportunity cost of money over time.