The problem describes an annuity where monthly payments of $100 are made, starting on January 31, with a yearly interest rate of 15%, compounded monthly. We are tasked with calculating the future value of the annuity on September 1, taking into account the compounded interest.

Let's break this down:

Formula for the Future Value of an Annuity:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

• FV: Future value of the annuity
• P: Payment per period ($100)
• r: Monthly interest rate (since the yearly interest rate is 15%, compounded monthly, the monthly interest rate is $r = \frac{15\%}{12} = 0.0125$)
• n: Number of payments (from January 31 to September 1 is 8 months)

Steps:

1. Monthly interest rate: 0.0125 (since the yearly rate is 15%)
2. Number of payments: 8 (one for each month from January 31 to September 1)
3. Substitute the values into the formula.

I'll calculate that now.The future value of the annuity on September 1 is approximately $835.89 (rounded to the nearest cent).

Would you like further details or have any questions?

Here are 5 related questions you might find helpful:

1. How is the future value of an annuity different from the present value?
2. What is the impact of increasing the interest rate on the future value?
3. How would the future value change if the compounding were done quarterly instead of monthly?
4. How would the calculation change if the payments were made at the beginning of each period instead of the end?
5. How is the formula for the future value of an annuity derived?

Tip: The more frequent the compounding period (e.g., monthly vs. quarterly), the greater the effect of interest on the future value of the annuity.