Figuring out compounding interest

  • Thread starter drymetal
  • Start date
  • Tags
    Interest
In summary, the conversation discusses the use of Excel and complicated formulas in investing money. The speaker is looking for a simpler way to calculate returns on investments, but is having trouble understanding their own formula and is seeking help to simplify and understand it. The conversation also mentions using a spreadsheet for more accurate and flexible calculations.
  • #1
drymetal
7
0
I talk to people a lot about the power in investing their money. I've always relied on Excel to figure out things though and I'm getting sick of it. So I figured there was a way to do it simpler with math than making gigantic lists that detailed every month and year a person invests money.

So, let's say I have 10,000 and will expect an 8% yearly return on it. I figured out a formula or whatever that will give me the correct answer quickly:

10,000 * 1.08^n

Or say it was for 20 years: 10,000 * 1.08^20

This is great. But it doesn't do a whole lot because people generally contribute money regularly to their investments. Which gets me to my question...


I wanted to keep it simple. Let's say a person has $100. They invest it and can expect to earn 8% every year. Additionally, they add an additional $100 every year. The answer I got in Excel was $4,044.63 after 18 years.

After countless months beating my head against a wall and talking to my cat, I came up with this:

100(1+.08)18+100[((1+.08)18-1)/.08]

However, that equals $4,144.63. And to be honest, I don't remember how the heck I came up with that crazy looking equation. :(

But, it is giving me the wrong answer! By $100! I must be doing something right. lol

Can anyone help me simplify and understand this? Thanks!
 
Mathematics news on Phys.org
  • #2
Your formula is correct, the difference is that you are assuming that the person invests $10,000 plus an additional $100 on day one. The formula that excel uses is starting the yearly $100 investments at the end of the first year.
 
  • #3
I don't understand. Is there just a regular formula with x's and y's and all those happy letters that does this? You know, where I can just plug the numbers in. The formula above I forgot how I came up with it.

The answer isn't as important to me as understanding it. Not that I don't want an answer - I do. But I need to understand it. Understanding it is paramount to me. I hope by learning the why - I can figure out equations on my own easier in the future.
 
  • #4
If the yearly investment and the interest rate are fixed, you could use power series to solve this:

let a = 1.08

you want to calculate the sum a^18 + a^17 + ... + a^1

multiply by a = a^19 + a^18 + ... a^2

subtract the original equation:

Code:
 a^19 + a^18 + ... + a^2
            a^18 + ... + a^2 + a^1
--------------------------------
 a^19                            - a^1

So the result is (a - 1)(a^18 + a^17 + ... + a^1) = (a^19 - a^1)

To get the original number divide by (a-1)

(a^18 + a^17 + ... + a^1) = (a^19 - a^1)/(a-1)

For your case you have 100 x (1.08^19 - 1.08) / (1.08 - 1) ~= 4044.6263239

Although this is nice for doing algebra, it's probably better to use a spread sheet, to handle variations in monthly deposits, changes in interest rates, and also allowing for interest that is compounded monthly (or daily) instead of yearly.
 
Last edited:
  • #5


I understand your frustration with trying to figure out compounding interest using Excel or complex equations. However, there are simpler mathematical formulas that can accurately calculate the growth of investments with regular contributions.

One such formula is the Future Value of an Annuity formula, which takes into account both the initial investment and regular contributions over a period of time. This formula is:

FV = P * [(1 + r)^n - 1] / r

Where:
FV = Future Value
P = Initial Investment
r = Interest Rate
n = Number of Periods

In your example, the initial investment is $100 and the regular contribution is also $100 per year, so the formula would be:

FV = $100 * [(1 + 0.08)^18 - 1] / 0.08

This gives a future value of $4,144.63, which matches your Excel calculation.

To understand why your initial equation gave a slightly different value, it's important to note that compounding interest is calculated based on the previous balance, not the initial investment. So, the correct formula would be:

FV = P * (1 + r)^n + C * [(1 + r)^n - 1] / r

Where:
FV = Future Value
P = Initial Investment
r = Interest Rate
n = Number of Periods
C = Regular Contribution

In your case, C = $100 and P = 0, so the second part of the equation becomes:

$100 * [(1 + 0.08)^18 - 1] / 0.08 = $144.63

Adding this to the initial investment of $100 gives a total of $4,144.63, which again matches the correct formula.

I hope this helps to simplify and understand the calculations for compounding interest. It's important to remember that regular contributions play a significant role in the growth of investments and should not be overlooked in calculations.
 

FAQ: Figuring out compounding interest

1. What is compounding interest?

Compounding interest is a type of interest calculation where the interest earned on an investment or loan is added to the principal amount, and then interest is calculated on the new total. This results in the interest earning interest, allowing for faster growth of the investment or larger amount owed on the loan.

2. How is compounding interest different from simple interest?

Simple interest is calculated only on the initial principal amount, while compounding interest takes into account the interest earned on the principal as well. This means that compounding interest will result in a higher return or a larger amount owed compared to simple interest.

3. What factors affect compounding interest?

The two main factors that affect compounding interest are the interest rate and the compounding frequency. The higher the interest rate, the more interest will be earned, and the more frequently the interest is compounded, the faster the growth or increase in the amount owed.

4. How can I calculate compounding interest?

To calculate compounding interest, you will need to know the principal amount, the interest rate, and the compounding frequency. You can use the formula A = P(1+r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

5. How can I use compounding interest to my advantage?

Compounding interest can be a powerful tool for growing your savings or investments over time. By choosing investments with higher interest rates and more frequent compounding periods, you can maximize your earnings. However, it's important to also be aware of the potential for compounding interest to increase the amount owed on loans, so it's important to manage debt carefully.

Similar threads

Replies
1
Views
2K
Replies
3
Views
1K
Replies
2
Views
2K
Replies
9
Views
2K
Replies
2
Views
7K
Replies
5
Views
2K
Back
Top