SOLUTION: The Pireras are planning to go to Europe 4 years from now and have agreed to set aside $180/month for their trip. If they deposit this money at the en each month into a savings acc

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: The Pireras are planning to go to Europe 4 years from now and have agreed to set aside $180/month for their trip. If they deposit this money at the en each month into a savings acc      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1209929: The Pireras are planning to go to Europe 4 years from now and have agreed to set aside $180/month for their trip. If they deposit this money at the en each month into a savings account paying interest at the rate of 3%/year compounded monthly, how much money will be in their ‘travel fund at the end of the fourth year? (Round your answer to the nearest cent.)
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Let's break down this problem step by step.
**1. Understand the Problem**
* This is a future value of an ordinary annuity problem.
* The Pireras deposit $180 at the end of each month.
* The interest rate is 3% per year, compounded monthly.
* The time period is 4 years.
**2. Identify the Variables**
* Monthly payment (PMT) = $180
* Annual interest rate (r) = 3% = 0.03
* Monthly interest rate (i) = r / 12 = 0.03 / 12 = 0.0025
* Number of years (t) = 4
* Number of payments (n) = t * 12 = 4 * 12 = 48
**3. Apply the Future Value of an Ordinary Annuity Formula**
The formula is:
FV = PMT * [((1 + i)^n - 1) / i]
Where:
* FV = Future Value
* PMT = Monthly Payment
* i = Monthly Interest Rate
* n = Number of Payments
**4. Calculate the Future Value**
FV = 180 * [((1 + 0.0025)^48 - 1) / 0.0025]
FV = 180 * [((1.0025)^48 - 1) / 0.0025]
Let's calculate (1.0025)^48 first:
(1.0025)^48 ≈ 1.1273383
Now, plug that into the formula:
FV = 180 * [(1.1273383 - 1) / 0.0025]
FV = 180 * [0.1273383 / 0.0025]
FV = 180 * 50.93532
FV ≈ 9168.3576
**5. Round to the Nearest Cent**
FV ≈ $9168.36
**Answer:** The Pireras will have approximately $9168.36 in their travel fund at the end of the fourth year.

Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

As it often happens with such calculations, the answer in the post by @CPhill is not accurate.
An accurate answer is $9167.62, obtained using MS Excel with 15 decimals and without making intermediate rounding.