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## Multiple transactions

**
Having reviewed the basics of interest, we now look at investments with multiple contributions and withdrawals, and develop a formula and a general purpose worksheet to calculate the performance over multiple 'terms'. **

- A formula would be ....

ClVal = Opval - Cost + Contris - Withdrls + Growth

- The big question is now.... how is Growth calculated

It is obviously % Growth on the Value Invested, which is the Opening Balance plus/minus transactions considered to be at the beginning of the period.

+ Although one might be tempted to include Contributions, is it for various reasons more logical to have all such transactions at the end of each term. So, we'll standardize on the principle that Contributions and Withdrawals are at the end of each period.

+ There is however one item that might need to be taken into account when calculating Growth, and that is Costs, since these are often raised at the beginning of each period, and hence deducted from the amount to be invested, another clever trick of investment companies.

- Expressing the above formula in the format of PV(1 + Growth Rate)

ClVal = OpVal - Costs + Contris - Withdrls + (OpVal - Costs)*Growth Rate

ClVal = (OpVal - Costs)(1 + Growth Rate) + Contris - Withdrls

Interesting..... This is a formula that I'll bet no-one every taught you

- Using the above formula we can create a bit of a worksheet to calculate the ClVal for one or more periods, given an OpVal, Costs, Contris, Withdrls and Growth Rate

Example showing multiple Contributions and Withdrawals

Growth Rate of 10%, digits after the point rounded
Period | OpVal | Costs | =InvestVal | Growth |
Contris | Withdrls | =ClVal | |

1 | 1000 | -20 | 980 | 98 | +100 | 0 | =1178 |

2 | 1178 | -30 | 1148 | 115 | 0 | -200 | =1063 |

3 | 1063 | -40 | 1023 | 102 | 0 | 0 | =1125 |

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