Setting up a fund

A child's grandparents decide to make a deposit at their grandchild's birth to provide for 5 annual payments of $3,000 starting it's 18th birthday, to pay for the child's education.

What sum should they set aside if the fund earns interest at 8 % compounded annually?

Answer: $3,237.32.

Lisa, who's 30 years old, wants to set up a retirement fund by depositing $100 into an account at the beginning of each month. When she gets 60 she plans to make monthly withdrawals over a period of 20 years.

How much will she be able to withdraw each month if interest is at 6.5 % compounded quarterly?

Step 1: Find the future value after 30 years.

Answer: After 30 years there will be $110,462.57 in the account.

Step 2: Find the monthly withdrawals that have a present value equal to that amount.

Answer: Lisa will be able to make a $816.91 withdrawal each month for 20 years before the account is empty.

Why is there such a big difference between the deposits and the withdrawals in the previous example?

The difference is due to the fact that while Lisa makes the withdrawals the remaining balance continues to generate interest.

Switching to the Single Payment calculation with $110,462.57 as the single payment value you can see in the details for the first period that this amount generates $595.13 as interest in just one month.

Furthermore you can switch to the Perpetuity calculation and enter $816.91 into the first payment field. Then you'll see that if there were $152,445.05 in the account withdrawals could continue indefinitely.