I started this quarter with £2,100 in my ISA, added £250 more, and yesterday I had £2,360.78 in my account.

The only investment I made this quarter, and since starting this ISA, was buying 75 shares of Provident Financial on August 24 for a total of £612.10, which are now worth £622.88, a profit of £10.78 and a return of 1.76% on this investment in a little over one month.

A couple of days after investing, the shares rose to over 940p, giving me a return of about 15%, and in the following days drifted down to almost 720p, giving me a loss of about 12% (I’m actually kind of bummed out because it didn’t crash even more; I would have liked buying more shares at 600p, and even more at 400p). It was only on Friday, September 29, that the share price once again rose above my purchase price, closing at 830.50p, otherwise I would have reported a loss for the quarter.

If I hadn’t added more money, calculating the total return on my ISA for the quarter would have been simple.** I would have started the quarter with £2,100 and ended with £2,110.78, for a total return of about 0.51%.** But I made more contributions at different dates, which will cause my true return to be a bit lower and makes calculating it a bit tricky (because I’m dealing with irregular cashflows).

**Compound interest formula**

A £1 profit on £10 invested one month ago doesn’t give me the same return as a £1 profit on £10 invested three months ago. In the first case, I have a return of 10% in one month, which is equivalent to an annual return of about 214%! In the second case, I have a return of 10% in three months, which is equivalent to an annual return of about 46%. How do I get these values, you ask? By using the compound interest formula:

Lets suppose I invest £10 and expect to get a 10% return in one year. £10 is the present value of my investment, 10% is the interest rate (r), and the number of times the interest is compounded is 1 (t). With this I can calculate the future value of my investment:

If I replace t with 12, to get the future value of £10 compounded at 10% per month a year from now, I get £31.38. A £21.38 profit on £10 is a return of about 214% in one year (£21.38/£10=2.138=213.8%). To get the future value of £10 compounded at 10% per quarter a year from now, I replace t with 4, and get £14.64. A £4.64 profit on £10 is a return of about 46% in one year (£4.64/£10=0.464=46.4%). Therefore, when and for how long you invest can matter a lot!

**Calculating the return on investments with irregular cashflows**

Below is my account history for this quarter:

I started July with £2,100 in my account. Usually I contribute another £50 every month, and I made an extraordinary contribution of £100 on September 17. Calculating the correct return on my total portfolio would require a lot of work because of this. Luckily, Excel has a function that does this for me in a few simple steps:** XIRR.**

Its syntax is **XIRR(values,dates,guess)**. ‘Values’ is a series of cashflows that correspond to a schedule of payments. Payments, or investments or cash inflows, are given a negative sign. Cash outflows are given a positive sign. ‘Dates’ is a schedule of payment dates that correspond to the cashflow payments. ‘Guess’ is a number that you guess is close to the result of XIRR, and is optional.

### Quarterly return

XIRR gives me the compounded annual growth rate of my ISA. Basically, it is the yearly equivalent of the return rate I achieved this quarter. So, how can I calculate my quarterly return? What rate, if compounded 4 times, gives me a return of 1,9855% at the end of one year?

Nothing to be excited about, as I had no great expectations since my portfolio is still 73.6% in cash, and my only investment was made about five weeks before the end of the quarter.

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