Figuring out compounding interest

by drymetal
Tags: compound, interest, math
 P: 7 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!  P: 11 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.
 HW Helper P: 7,134 Figuring out compounding interest 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:  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.