Following a weekend drive to Noosa on the Sunshine Coast to test out his new BMW X6 car, Mr Jack Bourne identified his ‘dream’ retirement home at the end of 2010. The property is currently (end 2010) valued at $850,000 and is likely to appreciate in value over the next 15 years (his anticipated retirement date from now) as follows:

-Years 1 to 5 by 8% p.a.,

-Years 6 to 10 by 10% p.a., and

-Years 11 to 15 by 15% p.a.

Jack is told by his financial advisor that he can earn a net 14% p.a. rate of return on any investment funds he puts aside to pay for his ‘dream’ retirement home over the 15 year term. Moreover, as a result of an inheritance from his grandfather, Jack also anticipates that he will be able to add a lump sum of $300,000 to these investment funds (used to pay for his retirement home) in 3 years from now.

Assuming that the actual amount paid by Jack at the end of 15 years to acquire his dream retirement home was $1.5m, calculate the annual rate of increase in the value of the property expressed as:

i) a nominal interest rate.

ii) an effective interest rate.