Investment Basics

If you are looking to invest your money in savings accounts, you may be considering regular savings accounts and fixed rate bonds.

These two products often have terms of one year. But they differ in that fixed rate bonds require all the money invested up front, whereas money must be invested in a regular savings account on a monthly basis.

What Is The Annual Return From A Regular Savings Account?

Suppose you wish to invest #100 a month in a regular savings account that pays 5.0% AER gross per annum. This will equate to #1,200 over a year.

The #100 that you invest in the first month will receive 12 months of interest, the #100 that you invest in the second month will receive 11 months of interest, and so on until your twelfth #100 investment will earn 1 month of interest.

Before we can compare the return from a regular savings account, with the return from a fixed rate bond, we need to do some sums to what out what return we'd get on our #1,200 over a one year period. The first step of this process is to calculate the regular saving account's monthly rate of interest, which is done with the following equation:

Monthly Interest = exp(ln(1.05)/12) -1 = 0.4074% per month

To check that this works, we can use a calculator to show that #100 x (1.004074) ^ 12 = 1.05.

So the first month receives earns (1.004^12-1 =) 5% interest over 12 months, the second month receives (1.004074^11-1 = ) 4.57% interest over 11 months etc... Those of you with a background in mathematics will recognise this as a geometric series. And to find the total return of this we need to sum the geometric series with this equation:

a(r^m - r^(n+1)) / (1-r).

To understand the equation, please search for Geometric Progression in Wikipedia. For our example, a=(1/12), r=1.004074, m=1 and n=12.

Note that we are investing one twelfth of our total invested capital a month. So plugging in the numbers we find that the AER of a 1.05% regular savings account, on the total capital invested, is 2.69% gross AER per annum. This is just over half of the 5%.

Please note that the money is fed into the savings account on a monthly basis. For example, you'll invest #1,200 over a year, but in the first month after you've only invested #100, you'll still have #1,100 that isn't invested. You could do something with that, such as investing it in an instant access account, which at time of writing might return 2.5% gross AER per annum.

The return from the instant access account with monthly returns is another geometric series, so the same equation can be used to calculate the interest earned on a 2.5% account if we withdraw one twelfth of the capital every month. But note that no interest is earned in the final month, as all capital will have been withdrawn (i.e. m=0, n=11). Plugging in the numbers gives us an AER of 1.14%.

So our total return on the #1,200 over a year will be 2.69% + 1.14% = 3.83%, which is a lot higher than the current best 1 year fixed rate of 3.2%.

First Direct And Santander Example

At time of writing, First Direct offer a regular savings rate of 8% on monthly investments from #25 to #300. This means that savers can invest up to #3,600 a year. Summing the geometric series, we find that a regular savings rate of 8% is equivalent to a 4.28% return on the total capital invested.

Santander offer a 2.75% Instant Access Account. Withdrawing one twelfth of the initial capital per month, would return 1.25% on the initial capital over a year.

Investors using both a First Direct regular savings account and Santander Instant Access Account, could therefore earn around 4.28% + 1.25% = 5.53% on balances of #3,600. That is a lot higher than the best one year fixed fixed rate bond rate.

Assuming the highest competing fixed rate is 3.00%, the extra 2.53% earned from this strategy is with #91.08 per annum!

Conclusion

This article has shown you how to convert a combined regular savings rate and instant access rate into an equivalent annual fixed rate. You can therefore use it to compare the two investment strategies.

Before you start opening accounts, please note that I have assumed that

- transfers between the instant access and regular savings account are instant.

- the instant access rate does not change.

- there are no withdrawal penalties from the instant access account.

Disclaimer: This article is for educational purposes only, and aims to help people think about their personal finances in more details. It may contain errors and the author takes no responsibility for any losses or problems incurred as a result of the information contained within the article. Do your own research before investing!

Imran Patel's articles on Fixed Rate Bonds Best Rates - 1 Year and One Year Fixed Rate Bonds Best Rates will help you to make more informed investment decisions.