https://file.aiquickdraw.com/mathbot/file/1726100062315ww9x0a44.jpg

answer the following question on the image

The question in the image involves calculating the size of equal quarterly payments needed to accumulate a total of R450,600 at the end of 12 years in a retirement fund that earns 14% annual interest, compounded quarterly.

### Key information:
- **Total amount to accumulate (FV)**: R450,600
- **Interest rate per year**: 14%
- **Compounding frequency**: Quarterly (4 times per year)
- **Time period**: 12 years
- **Payments made every quarter (4 times a year)**: To be determined (PMT)

### Formula to use:
This is a Future Value of an Annuity problem, where you make periodic payments into an account that earns interest. The formula for the future value of an annuity compounded periodically is:

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

Where:
- \(FV\) is the future value (R450,600),
- \(PMT\) is the quarterly payment (to be determined),
- \(r\) is the annual interest rate (14% or 0.14),
- \(n\) is the number of compounding periods per year (4 for quarterly),
- \(t\) is the total time in years (12).

We need to solve for \(PMT\).

Let me calculate the payment amount for you.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can manually use the future value of annuity formula to solve for the payment amount. If you need guidance on how to proceed, feel free to ask!

Would you like me to walk you through the manual calculation?

Here are 5 related questions for you to think about:
1. What happens if the interest rate changes to 10% instead of 14%?
2. How would the quarterly payment change if the time period was reduced to 10 years?
3. What if you wanted to accumulate a different amount, say R500,000, in the same timeframe?
4. How do monthly contributions affect the payment size compared to quarterly?
5. What is the impact of inflation on the future value of this retirement fund?

**Tip:** Always ensure the compounding frequency and payment periods match (e.g., quarterly compounding with quarterly payments).

You plan to make equal quarterly deposits at the end of every three months into your retirement fund. The fund earns 14% interest per year, compounded quarterly. You wish to have accumulated R450,600.00 at the end of 12 years. The size of each of the payments has to be:

Learn how to calculate the size of quarterly deposits to accumulate R450,600 in 12 years with a 14% interest rate compounded quarterly. This problem covers key finance concepts, including compound interest, annuities, and future value calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation