Ethan is responsible for managing a college endowment fund that received a donation of $200,000 at t=0. Ethan plans to let it grow untouched to maximize the returns until the college begins drawing equal annual payments from the fund at the end of t=5 to support scholarships for the next 10 years. The annual interest rate for the endowment is 5%. This cash flow has been deferred for how many periods? keep in mind this is a shifted series

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

Ethan is responsible for managing a college endowment fund that received a donation of $200,000 at t=0. Ethan plans to let it grow untouched to maximize the returns until the college begins drawing equal annual payments from the fund at the end of t=5 to support scholarships for the next 10 years. The annual interest rate for the endowment is 5%. This cash flow has been deferred for how many periods? Keep in mind this is a shifted series.

Explore the calculation of a deferred annuity for a college endowment fund that grows for 5 years at a 5% interest rate before making equal annual payments for 10 years. Learn how to determine the deferred period and apply the appropriate formulas for annuities and compound interest.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation