$($a$)$ You have kept aside RM$100,000$ in the bank to pay for your house renovation. Today, you received a bill from your contractor amounting to RM$60,000.$ At the same time, there is an investment offer from a reputable bank that you are highly considering. The investment opportunity promises the following returns:

Investment amount Return $($percent$)$

First RM$20,00016$

Next RM$20,00014$

Next RM$20,00011$

Next RM$20,0009$

Next RM$20,0008$

Suppose the market interest rate is $10$ percent per annum, based on the Fisher$$s

Theorem:

i$.$ Determine your investment tier.

ii$.$ Calculate your optimise return one year later.