https://file.aiquickdraw.com/mathbot/file/1728700929247bs7x0nn9.jpg

The problem asks to find the future value of an annuity due, given:

- Payment $ R = 16,000 $
- Interest rate $ i = 0.07 $ (7% compounded annually)
- Number of payments $ n = 8 $

The formula for the future value $ FV $ of an annuity due is:

\[
FV = R \times \left( \frac{(1 + i)^n - 1}{i} \right) \times (1 + i)
\]

Let's break it down:

1. Compute $ (1 + i)^n $.
2. Subtract 1 from that result.
3. Divide by $ i $.
4. Multiply by $ R $ and then by $ (1 + i) $.

Let me calculate that for you.The future value of the annuity due is approximately **$175,647.82**, rounded to the nearest cent.

Do you want further details on how this was calculated or have any questions?

Here are 5 related questions to deepen your understanding:

1. What is the difference between an annuity due and an ordinary annuity?
2. How does the compounding frequency affect the future value of an annuity?
3. What would happen to the future value if the interest rate was compounded semi-annually instead of annually?
4. How does increasing the number of payments (n) affect the future value of an annuity due?
5. What is the present value of this annuity due?

**Tip:** Always double-check if you're dealing with an annuity due or an ordinary annuity, as their future value formulas differ slightly due to the timing of the payments.

Find the future value of the following annuity due. Assume that interest is compounded annually, there are n payments of R dollars, and the interest rate is i. R = 16,000; i = 0.07; n = 8.

Learn how to calculate the future value of an annuity due with annual payments of $16,000, an interest rate of 7% compounded annually, and 8 payments. Detailed explanation with step-by-step breakdown of the annuity due formula.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation