Rachael also wishes to save for retirement. She can comfortably afford to invest R8 500 at the end of each month into an account which offers an interest rate of 10,7% per annum, compounded monthly,...

Rachael also wishes to save for retirement. She can comfortably afford to invest R8 500 at the end of each month into an account which offers an interest rate of 10,7% per annum, compounded monthly, for period of 20 years. After 20 years she wants to stop depositing R8 500 each month and intends to let the investment sum grow at 11,2% compounded quarterly until she has an amount of at least R26 000 000.

How long, correct to the nearest month, will it take to realise her goal?