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rmheins · Apr 12, 2007, 07:51 PM

1.)if you deposit money todayinto an account that pays 6.5% interest, how long will it take you to double your money?
2.) you have 42,180.53 in a brokage account and you plan to contribute an additional $5000.00 at the end of every year. The brokage account has an expected annual return of 12%. If your goal is to accumulate $250,000.00 in the account how long will it take you to reach your goal?
3.) what is the future value of a 5 year ordinary annuity that promises to pay you $300.00 each year?the rate of interest is 7%.
4.)what is the future value of a 5 year annuity due that promises to pay $300.00 each year?assume that all payment are reinvested at 7% a year until year 5?

goldenbutterfly · Apr 13, 2007, 01:43 AM

1. 72/6.5 = 11.07 years to double your money.

goldenbutterfly · Apr 13, 2007, 01:53 AM

Originally Posted by rmheins

1.)if you deposit money todayinto an account that pays 6.5% interest, how long will it take you to double your money?
2.) you have 42,180.53 in a brokage account and you plan to contribute an additional $5000.00 at the end of every year. The brokage account has an expected annual return of 12%. If your goal is to accumulate $250,000.00 in the account how long will it take you to reach your goal?
3.) what is the future value of a 5 year ordinary annuity that promises to pay you $300.00 each year?the rate of interest is 7%.
4.)what is the future value of a 5 year annuity due that promises to pay $300.00 each year?assume that all payment are reinvested at 7% a year until year 5?

2. 11 years

3. $1,725.22

4. $1,845.99

Capuchin · Apr 13, 2007, 01:53 AM

Goldenbutterfly used a rough rule, and gave a precise answer, a more accurate but less precise answer (if you want to know the difference between accuracy and precision in math, please ask me) would be "11".

Let me show you how to work it out without using the rule.

$1*1.065^{n} = 2$

This is the formula you need to solve to get the correct answer, you start with 1 dollar, the interest over n years is 1.065^n (100% + 6.5%, n times), and you want to end up with 2 dollars. All you need to do now is solve for n.

Get rid of the 1, it's useless:

$1.065^n = 2$

take logarithm of both sides:

$log1.065^n = log 2$

Use log rule to bring power out of the logarithm:

$n log 1.065 = log 2$

Rearrange logarithms:

$n = \frac{log 2}{log 1.065}$

Putting this into a calculatr, we get n = 11.008 years, which is quite a way off golden butterfly's answer, and is much more accurate. Goldenbutterfly, it's important to consider how accurate your answer is, and to put the right number of decimal places for the answer! '11' would have been much more accurate.

Now I have shown you how to work out the first one, see if you can work out the rest, they all work from the same principle, with a few simple complications thrown in.

Capuchin · Apr 13, 2007, 02:05 AM

Just because Goldenbutterfly didn't want to explain their use of 72 in the first question, I will give it here:

It's an old rule in finance called the rule of 72. There's also a rule of 71, rule of 70, and rule of 69.3, all of which are meant to deal with doubling of investment. They give very rough answers (72 is the one that is furthest off). As you can see, his use of the rule of 72 resulted in the answer being over .05 years off (over 20 days).

More information here: Rule of 72 - Wikipedia, the free encyclopedia

goldenbutterfly · Apr 13, 2007, 07:00 AM

To capuchin: Yes, you are correct. I am actually quite hesitant in giving out answers with complete explanations because I am thinking that these students must have been given the formulas in school. They have to exert some effort in solving them rather than relying too much on others by simply pasting the questions here.

Btw, your answer above is impressive. I was wondering why our math teacher did not teach us that!! :) thanks!

Capuchin · Apr 13, 2007, 07:18 AM

I'm glad that you realise, but if you give a student the answers, then they will learn nothing also. I think the approach I used of solving one question (or solving a similar, made up question) makes them have to learn to do the work.

goldenbutterfly · Apr 13, 2007, 07:28 AM

Maybe. But in the end it all boils down to the student's attitude.

Capuchin · Apr 13, 2007, 07:29 AM

Oh of course, and someone wh o posts a question like this, with no indication of even trying the question, probably doesn't have the best of attitudes :)