There is a very informative Wikipedia entry about the building at this URL - https://en.wikipedia.org/wiki/Mutual_Building. What is provided below is a very short summary. If you are at all interested in the details of the building you are strongly recommended to go to wikipedia.
The building was opened early in 1940 with a great fanfare. The local paper provided a 16 page supplement, and South African architects and dignitaries enthused about it.
The design of the building is attributed largely to Fred Glennie - not widely known outside Cape Town and South Africa, but well known locally at the time, especially for his work as mentor to a generation of architectural students, it seems.It is pleasing that the building has been so little changed over the years. Art Deco is not to everyone's taste, but as incorporated into the design of the Mutual Building it is very, very impressive. Dark marble in the entrance hall, shades of paler marble in the magnificent banking hall, and characteristic stainless steel trim and light fittings everywhere. When we get into the details, experts might argue that the different parts of the building are actually conceived in different styles. For example, the banking hall is said to be an example of 'neo-classicism' with tall marble clad colonnades; the entrance hall is quite different, severe, vertical and austere with its black marble walls and stainless steel fittings.
It is said that when opened, the building was the tallest in Africa with just one exception: the Pyramids in Egypt. You can see how it now compares with other tall buildings if you go to www.skyscrapers.com (the content of which now seems to have migrated to www.emporis.com) where there is an interesting catalogue of the world's tallest buildings. The figure at the right has been adapted from their web site, not only to show that the Old Mutual Building* in Cape Town is included in their listings, but that it compares favourably with some of the other tall buildings in the world. Yes, new buildings are now being built with almost 100 floors (or "storeys"), but if you do some simple sums with the data given in the figure you will find that of the three buildings depicted, The Old Mutual Building has the greatest span between floors - more than five metres. If you have been into the building, you will know about this. At all levels, the ceilings are very high, and in one of the meeting rooms on the eighth level the curtains alone are more than six metres long.
* According to the nomenclature on the outside of the building, it is properly known as "The Mutual Building" or "Mutual Gebou" (in Afrikaans). The developers who undertook the residential conversion in 2000 decided to name it 'Mutual Heights', but because of its association with the Old Mutual insurance business it is most commonly referred to as 'the Old Mutual Building'. This is despite the fact that Old Mutual began to vacate the building in the 1960s - only 20 years after it was completed!