SOLUTION: Twins graduate from college together and start their careers. Twin 1 invests $1500 at the end of each year for 10 years only (until age 31) in an account that earns 8%, compounded

Question 1198640: Twins graduate from college together and start their careers. Twin 1 invests $1500 at the end of each year for 10 years only (until age 31) in an account that earns 8%, compounded annually. Suppose that twin 2 waits until turning 40 to begin investing. How much must twin 2 put aside at the end of each year for the next 25 years in an account that earns 8% compounded annually in order to have the same amount as twin 1 at the end of these 25 years (when they turn 65)? (Round your answer to the nearest cent.)
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
**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.**

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