Question 1172706: As part of your retirement plan, you have decided to deposit $6,000 at the beginning of each year into an account paying 5% interest compounded annually. (Round your answers to the nearest cent.)
How much (in $) would the account be worth after 10 years?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Certainly! Let's break down how to calculate the future value of your retirement account.
**Understanding the Problem**
This is an example of an annuity due, where payments are made at the beginning of each period.
**Formula**
The formula for the future value (FV) of an annuity due is:
FV = P * [((1 + r)^n - 1) / r] * (1 + r)
Where:
* P = periodic payment ($6,000)
* r = annual interest rate (5% or 0.05)
* n = number of years (10)
**Calculation**
1. **Plug in the values:**
FV = 6000 * [((1 + 0.05)^10 - 1) / 0.05] * (1 + 0.05)
2. **Calculate (1 + 0.05)^10:**
(1.05)^10 ≈ 1.62889462678
3. **Calculate ((1 + 0.05)^10 - 1):**
1.62889462678 - 1 ≈ 0.62889462678
4. **Divide by 0.05:**
0.62889462678 / 0.05 ≈ 12.5778925356
5. **Multiply by 6000:**
12.5778925356 * 6000 ≈ 75467.3552136
6. **Multiply by 1.05:**
75467.3552136 * 1.05 ≈ 79240.7229743
7. **Round to the nearest cent:**
$79,240.72
**Answer**
The account would be worth approximately $79,240.72 after 10 years.
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