Final answer:
The present value of an annuity paying $10 annually for 98 years at a discount rate of 7% is calculated using the present value of an ordinary annuity formula. An example to illustrate the concept using a simple two-year bond shows how to discount future cash flows at different interest rates to determine present value.
Step-by-step explanation:
The question asks for the present value (PV) of an annuity that pays $10 per year for 98 years with a discount rate of 7%. To calculate the PV of the annuity, you can use the formula for the present value of an ordinary annuity:
PV = Pmt * [(1 - (1 + r)^-n) / r]
Where Pmt is the annual payment, r is the discount rate per period, and n is the number of periods.
In this case, Pmt is $10, r is 0.07 (7% expressed as a decimal), and n is 98. Plugging these values into the formula gives:
PV = $10 * [(1 - (1 + 0.07)^-98) / 0.07]
After doing the math, this calculation will yield the present value of the annuity. To calculate the present value of the two-year bond with different interest rates, similar principles of discounting future cash flows apply.
For example, if a two-year bond pays $3,000 at the end of the second year plus $240 interest annually at a discount rate of 8%, the calculation would look like this:
PV = $240 / (1 + 0.08) + ($240 + $3000) / (1 + 0.08)^2
And if the discount rate rises to 11%, you would instead use:
PV = $240 / (1 + 0.11) + ($240 + $3000) / (1 + 0.11)^2