ASSIGNMENT
Why does an annuity due always have a higher future value than an ordinary annuity?
If you calculated the value of an ordinary annuity, how could you find the value of the corresponding annuity due?
Assume that you plan to buy a condo five years from now, and yo need to save for a down payment. You plan to save $2,500 per year, with the first payment made immediately, and you will deposit the funds in a bank account that pays 4 percent. How much will you have after five years? How much would you have if you made the deposits at the end of each year? ($14,082.44; $13,540.81)
Why does an annuity due have a higher present value than an ordinary annuity?
If you know the present value of an ordinary annuity, how could you find the PV of the corresponding annuity due?
What is the PVA of an ordinary annuity with 10 payments of $100 if the appropriate interest rate is 10 percent? What would PVA be if the interest rate were 4 percent? What if the interest rate were 0 percent?
How would the PVA values differ if we were dealing with annuities due? ($614.46; $811.09; $1,000.00; $675.90; $843.53; $1,000)
Assume that you are offered an annuity that pays $100 at the end of each year for 10 years. You could earn 8 percent on your money in other investments with equal risk.
What is the most you should pay for the annuity? If the payments began immediately, how much would the annuity be worth? ($671.01; $724.69)
What’s the present value of a perpetuity that pays $1,000 per year, beginning one year from now, if the appropriate interest rate is 5 percent? What would the value be if the annuity began its payments immediately? ($20,000, $21,000. Hint: Just add the $1,000 to be received immediately to the value of the annuity.)
Would distant payments contribute more to the value of an annuity if interest rates were high or low? (Hint: When answering conceptual questions, it often helps to make up an example and use it to help formulate your answer. PV of $100 at 5 percent after 25 years $29.53; PV at 20 percent $1.05. So, distant payments contribute more at low rates.
