I am one hell of a confused guy when it comes to math. Well here is this problem I'm trying to figure out and I am supposed to explain it well, but I'm way too stuck to begin. Even if I knew how to start, I just seem to not understand. Anyways, here is the problem:
I am planning to buy a 2007 Audi A8 car that costs approximately $13,000 (just made up). There are a lot of ways to get enough money to buy the Audi (you only have $1000 in your piggy bank). Here are the ways:
1) A traditional loan
2) Putting $1000 into a savings account and letting interest happen until you've got enough money
3) Putting $1000 into some other type of investment account and letting interest happen until we've got enough money
AND
4) Putting $1000 into an account and letting interest happen but also putting another $50 into the account each month.
Okay it then tells me to visit a homepage of a bank and find two investment options that I'm interested in (Huh?).
Then determine how long it will take me to save up the amount of money that I need.
The final question is which of the ways is the best that will get to the amount of money I need to buy the car.
I know right, tough!!! Please help!!! Thank you, Math Help Forum members.
I dont know of any sites off the top of my head, but here's how to do the problem.
You use the formula A(t) = A0*e^(rt), where A(t) is the amount of money you have at a given time, A0 is the amount of money you started with, r is the rate of interest, and t is the time.
In your case, A(t) = 13000, A0 = 1000, r = ?, t = ?
So you will have 4 different r's coressponding to the 4 options you gave. Plug each into the formula 13000 = 1000*e^(rt) or equivalently, 13 = e^(rt) which you would have to solve using logarithims.
if you have r, you can solve for the time t. So the one with the smallest t will be best for getting the loan paid of as soon as possible. If you want to specify a time, then you would solve for r. The one with the lowest r is more affordable.
Thanks for the quick reply. Could you possibly make up a number for loans or anything else that I need to simple this problem out for me. I was looking everywhere on Google to find loans or anything for the problem but it was driving me crazy. Could anyone make something up for 'r' and 't'?
Thanks again, Jhevon, for helping me out.
Haha, ok, that's not realistic. if you just dump 1000 in an account and forget about it, it will have to have an interest rate of 42.75% a month, which you won't find.
You will be able to find interest rates around 4%, which means it will take you about 64.12 months to pay it off, if the interest is compounded continuously.
If you take the last option, that is, put in 1000 to start and giving $50 per month, it will take you 46.13 months to pay it off, if its compounded continuously at 4% interest.
If we are really to help you, you have to give us the actual loans that you are thinking about, and we'll tell you what's best.
These quotes that i'm giving you are worst case senario. i doubt any bank compouds an account or a loan continuously, they probably do it by-yearly, or annually. in which case we need to know how the interest grows, and the interest rate (or time you want to pay it off in) to help you