Question 1198640
**1. Calculate the Future Value of Twin 1's Investments**

Twin 1 is making annual investments of $1500 for 10 years at an 8% annual interest rate. This is an ordinary annuity. 

* **Future Value of Annuity:** 
    * FV = P * (((1 + r)^n) - 1) / r 
        * where:
            * FV = Future Value
            * P = Periodic Payment ($1500)
            * r = Interest Rate per period (0.08)
            * n = Number of periods (10 years)

* **Calculate FV for Twin 1:**
    * FV = 1500 * (((1 + 0.08)^10) - 1) / 0.08 
    * FV ≈ $21,729.84

**2. Calculate the Required Annual Investment for Twin 2**

Twin 2 needs to accumulate the same future value ($21,729.84) in 25 years with the same 8% interest rate.

* **Rearrange the Future Value of Annuity formula to solve for the periodic payment (P):**
    * P = FV * (r / ((1 + r)^n) - 1))

* **Calculate the required annual investment for Twin 2:**
    * P = 21729.84 * (0.08 / ((1 + 0.08)^25) - 1))
    * P ≈ $297.24

**Therefore, Twin 2 needs to invest approximately $297.24 at the end of each year for the next 25 years to have the same amount of savings as Twin 1 at age 65.**