# Math Help - Compound Interest Savings Account

1. ## Compound Interest Savings Account

Hi All

I am new to this forum, so I hope you would not mind the links in this message as I needed to list them to explain my query.

I design, develop and host online graphing, scientific, statistical and financial calculators at http://www.thinkanddone.com

That said, I was working on design of a Savings Account calculator that I need help with formulas. Doing a search on web, I found Professor Grant Lythe's (Uni of Leeds) notes

Example

Let us consider the example of a savings account that pays 6% interest compounded monthly. Suppose a saver deposits $1000 on the first day of every month. What is the account balance at the end of 2 years I found the following formula to compute the balance at end of n period r is the interest rate p = 1 + (1/12)(r/100) A = 1000 p ( (p^n)-1 )/(p-1) A = 25559.12 I compared my results to an online calculator at Savings Calculator - Financial Calculators from Dinkytown.net So far so good. But like the calculator, I am trying to compute balance by changing either the compounding period to daily, quarterly and yearly or the deposit interval to weeky, biweekly, per quarter and per year How can I change the formula I mentioned at top for these option I will post a different question about continuous compounding of interest as the calculators I used on Aussie bank sites show different answer to the result above so I assume they use continuous compounding of interest . ( Finance calculators - financial comparisons and information from Infochoice ) 2. Originally Posted by dexteronline Let us consider the example of a savings account that pays 6% interest compounded monthly. Suppose a saver deposits$1000 on the first day of every month. What is the account
balance at the end of 2 years

I found the following formula to compute the balance at end of n period

r is the interest rate
p = 1 + (1/12)(r/100)
A = 1000 p ( (p^n)-1 )/(p-1)
A = 25559.12

But like the calculator, I am trying to compute balance by changing either the compounding period to daily, quarterly and yearly
or the deposit interval to weekly, biweekly, per quarter and per year

How can I change the formula I mentioned at top for these option
$
\ddot S = R \cdot \frac{{\left( {1 + {\textstyle{j \over m}}} \right)^{tm} - 1}}{{{\textstyle{j \over m}}}} \cdot \left( {1 + {\textstyle{j \over m}}} \right) = 1,000\frac{{\left( {1 + {\textstyle{{.06} \over {12}}}} \right)^{2 \times 12} - 1}}{{{\textstyle{{.06} \over {12}}}}} \cdot \left( {1 + {\textstyle{{.06} \over {12}}}} \right)
$

To compute balance by changing either the compounding period to daily, quarterly and yearly, just change m to 365, 4, and 1. Make sure the deposit interval is the same as the interest compounding/conversion period.
If not, contemplate this.

3. ## I had come to the right forum: Thanks Jonah

Jonah

The continuous compounding formula is what the banks in Australia are using for their Savings Calculator at Bank of Queensland, Savings calculator

And your provided formula produces the result, how would I adjust this continuous compounding formula if there is an initial invest along with periodic deposits. Say an initial deposit of $2000 and monthly payments of$1000 for 2 years at 6%

Jonah I have been developing these online tools for the last two years, I had converted on of them to Desktop Version which allows graphing f(x) in coordinate plane, Here is where you can download it http://www.thinkanddone.com/ge/GraphEasyRect.jar

You would need Java Runtime Environment to be installed for the program to run MS Windows, Linux or Mac OS .

This forum has opened new venues for me. As I am always looking for new ideas to develop calculator, now I know where to get help when looking for help with formulas

4. Originally Posted by dexteronline
And your provided formula produces the result, how would I adjust this continuous compounding formula if there is an initial invest along with periodic deposits. Say an initial deposit of $2000 and monthly payments of$1000 for 2 years at 6%
If the monthly payments of $1000 were made at the beginning of every month and your nominal rate of 6% is compounded continuously, then $ 2,000e^{0.06 \times 2} + 1,000\frac{{e^{0.06 \times 2} - 1}}{{e^{{\textstyle{{0.06} \over {12}}}} - 1}} \cdot e^{{\textstyle{{0.06} \over {12}}}} $ If the monthly payments of$1000 were made at the end of every month, then

$
2,000e^{0.06 \times 2} + 1,000\frac{{e^{0.06 \times 2} - 1}}{{e^{{\textstyle{{0.06} \over {12}}}} - 1}}
$

You might want to check this and this out for a more comprehensive layout. You can read them online (disadvantage: a few pages are missing) or you can order them online.

The fourth edition of Dr. Broverman's book with its corresponding solutions manual is now available. Just follow the threads.

5. ## Thanks Jonah

Jonah

Thanks for taking time to answer my questions. I think these books will be of great help