You are set to receive an annual payment of $12,100 per year for the next 17 years. Assume the interest rate is 7 percent. How much more are the payments worth if they are received at the beginning of the year rather than the end of the year?

Multiple Choice

$7,364.98

$7,752.61

$8,269.45

$8,011.03

$8,682.92

This problem involves calculating the present value (PV) of an annuity and comparing the difference between an **annuity due** (payments at the beginning of the year) and an **ordinary annuity** (payments at the end of the year).

### Steps to solve:

1. **Ordinary Annuity Formula (End of the Year Payments):**
   \[
   PV = P \times \left(1 - (1 + r)^{-n} \right) / r
   \]
   Where:
   - $ P = 12,100 $ (annual payment)
   - $ r = 0.07 $ (interest rate)
   - $ n = 17 $ (number of years)

2. **Annuity Due Formula (Beginning of the Year Payments):**
   The present value of an annuity due can be calculated using the ordinary annuity formula and multiplying it by $ (1 + r) $:
   \[
   PV_{\text{due}} = PV_{\text{ordinary}} \times (1 + r)
   \]

3. **Difference Between Annuity Due and Ordinary Annuity:**
   Finally, subtract the present value of the ordinary annuity from the present value of the annuity due to find how much more the annuity due is worth.

Let's calculate.The payments are worth **$8,269.45** more if they are received at the beginning of the year rather than the end of the year.

The correct answer is: **$8,269.45**.

Would you like more details on how this was calculated or have any further questions?

Here are 5 related questions for further understanding:
1. What is the difference between an ordinary annuity and an annuity due?
2. How does the interest rate affect the present value of annuities?
3. What happens to the present value if the number of years increases?
4. Can you explain how to calculate the present value for other interest rates?
5. How would inflation impact the value of future payments?

**Tip:** An annuity due always has a higher present value than an ordinary annuity, since payments are received earlier, benefiting from extra interest accrual.

You are set to receive an annual payment of $12,100 per year for the next 17 years. Assume the interest rate is 7 percent. How much more are the payments worth if they are received at the beginning of the year rather than the end of the year?

Learn how to calculate the present value difference between an annuity due and an ordinary annuity, given an annual payment of $12,100 for 17 years at an interest rate of 7%. This solution provides detailed steps to solve using key formulas for present value and interest rates.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation