You have ​$200,000 to donate to your college. The​ college's discount rate is 11​%. You donate the money​ today, but you ask the college to delay the scholarship payment so that the first scholarship payment is made 10 years from today. How large will the annual payment​ be?

To determine the size of the annual scholarship payment, we need to calculate the present value of an annuity, where the total donation of $200,000 grows at a discount rate of 11% over the 10-year delay before the first payment is made. Here’s the approach:

1. **Formula**:  
   The present value of an annuity is given by:

   \[
   PV = \frac{A}{r} \left[ 1 - \frac{1}{(1 + r)^n} \right]
   \]
   where:
   - $ PV $ is the present value (which is $200,000 in this case),
   - $ A $ is the annual payment,
   - $ r $ is the discount rate (11%, or 0.11),
   - $ n $ is the number of years for the payments (since we are delaying the scholarship for 10 years, we would typically calculate the present value 10 years in the future).

2. **Adjusting for the Delay**:  
   Since the first payment is made 10 years from now, we need to adjust the present value for the fact that the college will only start using the fund 10 years later. We’ll first calculate the future value of the $200,000 in 10 years using the formula:

   \[
   FV = PV \times (1 + r)^n
   \]
   This gives the future value of the donation at the time the scholarship payments begin.

Let’s calculate the future value first and then the corresponding annual payments.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, you can use the following steps to calculate the solution manually:

### Step-by-step instructions:
1. **Future Value Calculation**:
   Use the formula:
   \[
   FV = 200,000 \times (1 + 0.11)^{10}
   \]
   This gives the future value of the donation 10 years from now.

2. **Determine Annual Payment**:
   Once you have the future value (FV), you can then calculate the annuity payments based on how many years the scholarship will last.

Let me know if you want more clarification or if you'd like to retry later!

Here are some related questions to explore:
1. What happens if the discount rate changes in the middle of the period?
2. How would the annual payment change if you donated the money earlier?
3. Can you calculate how much the future value will be if you change the donation amount?
4. What are the implications of changing the time period from 10 years to 5 years?
5. How does the discount rate influence the time value of money?

**Tip**: Always break down complex financial calculations into smaller steps to avoid confusion and errors.

You have $200,000 to donate to your college. The college's discount rate is 11%. You donate the money today, but you ask the college to delay the scholarship payment so that the first scholarship payment is made 10 years from today. How large will the annual payment be?

Discover how to calculate the size of annual scholarship payments using a $200,000 donation delayed by 10 years with an 11% discount rate. This problem involves key financial concepts like the present value of annuities and future value calculations, suitable for undergraduate finance students.

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