<p>What you need is the future value of an annuity. If you have a payment P paid for N years, compounding at an interest rate i, the future value of that is: </p>

<p>$FV=P*( (1+i)^N - 1)/i$</p>

<p>This will give you the future value at the beginning of the year. To get it for the end you multiply with (1+i). In your example filling in P=8000, i=10%, and N=2 gives you 16800, which when multiplied with 1.1 gives you the desired 18480.</p>

CC BY-SA 3.0
2018-03-14T13:29:49.437Z
how did you derrive this formula?
KarmaPeasant
CC BY-SA 3.0
2018-03-14T13:41:15.137Z
I tried your formula with my example. Doesn't seem to work. Please show me how to correctly use it to get  $18480 given situation in my example.
KarmaPeasant
CC BY-SA 3.0
2018-03-14T16:28:31.123Z
The formula gives you the beginning of the year sum. Multiply with (1+i) to get the end of year sum. I have edited my answer.
Maarten Punt
CC BY-SA 3.0
2018-03-14T12:44:03.880Z
2018-03-14T16:27:27.730Z
2018-03-14T16:27:27.730Z
Maarten Punt
<p>For example:</p>

<p>Let's suppose that at the end of the first year I got \$8 000  of revenue (like I have a business or something). I put the money in a bank at the beginning of the second year, annual percentage rate was 10% (from now on I assume that the annual percentage rate will remain the same). At the end of the second year there were \$8 800 on my bank account, but I added \$8 000 to it at the beginning of the third year, thus at the end at the end of the third year I had \$18480 on my bank account, instead of \$9680. I continue to replenish my bank account every year by \$8 000 (inflation is ignored), until the beginning of year number N, when I will do it for the last time. I want to know what sum of money I will have at the end of year number N.</p>

CC BY-SA 3.0
2018-03-14T10:40:55.787Z
What exactly is stopping you from calculating the sum of this geometric sequence?
Giskard
CC BY-SA 3.0
2018-03-14T10:42:20.863Z
This seems like it is off-topic. Perhaps you can try posting it on the Personal Finance SE, but I would recommend just crunching numbers in Excel, Google Docs or Open Office.
Giskard
CC BY-SA 3.0
2018-03-14T11:37:44.860Z
This isn't related to personal finances, I came up with it when I were trying to solve a problem from my microeconomic textbook. And I would prefer either formula or algorithm over "blackbox" function of spreedsheet program. "What exactly is stopping you from calculating the sum of this geometric sequence?" I have no idea how to derrive it. Could you please give me the formula for this sum of geometric sequences, if you already know?
KarmaPeasant
CC BY-SA 3.0
2018-03-14T14:06:48.740Z
[Sure](http://lmgtfy.com/?q=sum+of+geometric+sequences)!
Giskard
CC BY-SA 3.0
2018-03-14T14:30:26.640Z
Hmm... After looking close, I don't see how it's helpful because I don't see how it accounts for regular replenishments of bank account from my side (no pun intended).
KarmaPeasant
CC BY-SA 3.0
2018-03-14T16:47:07.180Z
I'm voting to close this question as off-topic because it does not concern the discipline of economics.
Giskard
CC BY-SA 3.0
2018-03-14T18:38:32.007Z
This formula can help to decide if something is a good investment. Like  "Should I buy this machine that yields $8 000 each year, considering that I can put the revenue in the bank and periodically add money to my bank account?"
KarmaPeasant
<interest-rate>
I want formula for compund interest with regular and fixed replenishments
KarmaPeasant
# I want formula for compund interest with regular and fixed replenishments

(Asked by: username_0 on 2018-03-14)

For example:

Let's suppose that at the end of the first year I got \$8 000 of revenue (like I have a business or something). I put the money in a bank at the beginning of the second year, annual percentage rate was 10% (from now on I assume that the annual percentage rate will remain the same). At the end of the second year there were \$8 800 on my bank account, but I added \$8 000 to it at the beginning of the third year, thus at the end at the end of the third year I had \$18480 on my bank account, instead of \$9680. I continue to replenish my bank account every year by \$8 000 (inflation is ignored), until the beginning of year number N, when I will do it for the last time. I want to know what sum of money I will have at the end of year number N.

**Tags:** interest-rate

> **Comments:**
> **username_1**: What exactly is stopping you from calculating the sum of this geometric sequence?  
> **username_1**: This seems like it is off-topic. Perhaps you can try posting it on the Personal Finance SE, but I would recommend just crunching numbers in Excel, Google Docs or Open Office.  
> **username_0**: This isn't related to personal finances, I came up with it when I were trying to solve a problem from my microeconomic textbook. And I would prefer either formula or algorithm over "blackbox" function of spreedsheet program. "What exactly is stopping you from calculating the sum of this geometric sequence?" I have no idea how to derrive it. Could you please give me the formula for this sum of geometric sequences, if you already know?  
> **username_1**: [Sure](http://lmgtfy.com/?q=sum+of+geometric+sequences)!  
> **username_0**: Hmm... After looking close, I don't see how it's helpful because I don't see how it accounts for regular replenishments of bank account from my side (no pun intended).  
> **username_1**: I'm voting to close this question as off-topic because it does not concern the discipline of economics.  
> **username_0**: This formula can help to decide if something is a good investment. Like  "Should I buy this machine that yields $8 000 each year, considering that I can put the revenue in the bank and periodically add money to my bank account?"  

---

## 1 answers

### Answer by username_2 on 2018-03-14. Score: 1

What you need is the future value of an annuity. If you have a payment P paid for N years, compounding at an interest rate i, the future value of that is:

$FV=P\*( (1+i)^N - 1)/i$

This will give you the future value at the beginning of the year. To get it for the end you multiply with (1+i). In your example filling in P=8000, i=10%, and N=2 gives you 16800, which when multiplied with 1.1 gives you the desired 18480.

> **Comments:**
> **username_0**: how did you derrive this formula?  
> **username_0**: I tried your formula with my example. Doesn't seem to work. Please show me how to correctly use it to get  $18480 given situation in my example.  
> **username_2**: The formula gives you the beginning of the year sum. Multiply with (1+i) to get the end of year sum. I have edited my answer.  

---

