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Question 280377: Jason Thomas has saved $2,500 towards a down payment on a new truck. He wants to have a total of $25,000 and plans to buy in 3 years. How much will he have to save at the end of each month if he can earn 5% on his savings?
Significant digits not applicable; exact number, no tolerance
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! He already has 2500 dollars.
If he saves his money with monthly compounding, that will be worth 2903.680578 at the end of 3 years from today.
Since he wants to have a total of 25000 in 3 years, then we subtract this from 25000 to get 22096.31942 which is the additional money he will need in 3 years.
Assuming monthly compounding, he would need to make payments of 570.1785182 per month for 36 months to equal 22096.31942 at the end of 3 years.
Today he has 2500 which will be worth 2903.6805787 in 3 years.
He is making monthly payments of 570.1785182 at the end of each payments that will be worth 22096.31942 in 3 years assuming he re-invests the interest the account is earning at the end of each month.
2903.6805787 + 22096.31942 = 25000 total he will have at the end of 3 years.
This does not take into considerations taxes on the money earned which puts a whole new dimension on the calculations required.
I used a financial calculator to provide the answers but there are formulas you can apply if you don't have access to one.
I have lessons on algebra.com for future value of a present amount and payment for a future value that contains the formulas.
Those lessons can be found by clicking on the following links.
Future Value of a Present Amount
Payment for a Future Value
When you get into Algebra.com, you can scan down the main page until you find "lessons" and click on that to get to the lessons.
All lessons written by all tutors on algebra.com can be found by clicking on the following link.
Alebra.com Lessons
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