Final answer:
To find the present value of an annuity or bond, discount each future payment to its present value and sum those values. This will give the total present value of the annuity or bond at a specified discount rate. Repeat the process with different rates as necessary to see how the present value changes.
Step-by-step explanation:
To find the present value of an ordinary annuity, you need to discount each future payment back to its present value and then sum up all these present values.
Let's consider the two-year bond example, issued at $3,000 with an 8% annual interest rate. The bond would pay $240 in interest each year, and the principal amount of $3,000 at the end of the second year.
To calculate the present value if the discount rate is 8%, you would use the formula:
- Present Value of Year 1 Interest = $240 / (1 + 0.08) = $240 / 1.08
- Present Value of Year 2 Interest + Principal = ($240 + $3,000) / (1 + 0.08)²
Summing these two amounts gives you the total present value at an 8% discount rate.
If the discount rate rises to 11%, repeat the calculations with 0.11 as the discount rate:
- Present Value of Year 1 Interest = $240 / (1 + 0.11)
- Present Value of Year 2 Interest + Principal = ($240 + $3,000) / (1 + 0.11)²
Again, sum the two amounts to find the total present value at an 11% discount rate.