To determine how many periods the cash flow has been deferred for, we need to carefully analyze the situation in the context of a shifted or deferred annuity.

Problem Recap:

• A donation of $200,000 is made at $t = 0$.
• The donation will grow for 5 years until the end of $t = 5$, without any withdrawals.
• After $t = 5$, the college will start withdrawing equal annual payments for the next 10 years to fund scholarships.
• The interest rate is 5% per annum.

Understanding the Deferred Annuity:

The cash flows (annual withdrawals) will start after a delay of 5 periods (years). In a deferred annuity, the number of deferred periods is the time between $t = 0$ (when the endowment fund begins) and the first payment (when withdrawals start).

• The payments will start at the end of $t = 5$, meaning the first payment happens after 5 full years.
• This makes the deferred period equal to 5 periods.

Thus, the cash flow has been deferred for 5 periods.

Would you like a deeper explanation of the concept of deferred annuities or any additional details?

Related Questions:

1. How do you calculate the value of the endowment at the end of the 5-year deferred period?
2. What formula can be used to compute the equal annual withdrawals for the 10 years?
3. How does the 5% interest rate affect the growth of the endowment fund?
4. What is the present value of the deferred annuity starting at ( t