Find the future value for the annuity due with the given rate.

Payments of $12,000 for 14 years at 0.26% compounded monthly

The future value of the annuity due

The future value of an annuity due can be calculated using the following formula:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the payment amount per period.
- $r$ is the interest rate per period.
- $n$ is the total number of payments.

### Given dataThe future value of an annuity due can be calculated using the following formula:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the payment amount per period.
- $r$ is the interest rate per period.
- $n$ is the total number of payments.

### Given 
- Payment ($P$) = $12,000
- Time = 14 years
- Interest rate per year = 0.26% per month compounded monthly (0.0026 annually).
- Compounding monthly, so the number of periods per year = 12.
  
Let's calculate:
1. Monthly interest rate ($r$):  
   \[
   r = \frac{{0.26\%}}{12} = \frac{0.0026}{12} = 0.00002167
   \]
   
2. Total number of payments ($n$):  
   \[
   n = 14 \times 12 = 168
   \]

Now, plugging these values into the formula:

\[
FV = 12,000 \times \left( \frac{{(1 + 0.00002167)^{168} - 1}}{0.00002167} \right) \times (1 + 0.00002167)
\]

Let me calculate this for you.The future value of the annuity due is approximately **$2,053,358.80**.

Would you like more details or further clarification?

Here are 5 related questions for deeper understanding:
1. How does the future value of an ordinary annuity compare to an annuity due?
2. What is the impact of changing the interest rate on the future value of an annuity?
3. How would a change in the payment frequency affect the future value?
4. Can you calculate the present value of an annuity due with the same parameters?
5. How does compounding frequency affect the future value of an annuity?

**Tip:** In an annuity due, payments are made at the beginning of each period, which slightly increases the future value compared to an ordinary annuity.

Find the future value for the annuity due with the given rate. Payments of $12,000 for 14 years at 0.26% compounded monthly.

Learn how to calculate the future value of an annuity due with payments of $12,000 over 14 years at an interest rate of 0.26% compounded monthly. This detailed solution covers financial mathematics concepts, including annuity due 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