You are considering the purchase of a property today for $$300,000.$ You plan to finance it with an $80$ percent loan. The appreciation rate on the property value is expected to be $4$ percent annually for the next three years.

Required:

a$.$ Approximate the expected annual average rate of appreciation on home equity for the next three years.

b$.$ What if you now think that a $$300,000$ purchase price may be somewhat high and that if you pay this price, the expected appreciation rates in your house price will be as follows: year $1=0\%,$ year $2=2\%,$ and year $3=3\%.$ Approximate the expected annual average rate of appreciation on home equity for the next three years.