211.3 & 4
3. Let's say that you expect to work for another 40 years. How much would you need to deposit today to set up an account that would pay $1000 per year forever, starting one year from your retirement (after you die, it would be split among your heirs). The relevant interest rate is 8%. (2 pts.)
This is a deferred perpetuity. First calculate the value of the perpetuity as if you were
retiring today:
Then figure out its value today, 40 years prior to your retirement:
4. Which of the following two changes to the above would each force you to make a larger deposit AND WHY? (1 pt.)
--you expect to retire sooner and interest rates are higher
--you expect to retire later and interest rates are higher
--you expect to retire sooner and interest rates are lower
--you expect to retire later and interest rates are lower
Expecting to retire sooner and having lower interest rates would each force you to
make a larger deposit today. If you expect to retire sooner, your deposit has less time to
grow to the $12,500 it must be in order to establish the perpetuity. If interest rates are
lower, the money you will deposit today will grow slower and the amount you will need in
order to establish the perpetuity will be bigger. That would force you to deposit more
today.