\($3,000\) is invested for \(18\) months compounded at the interest rate of \(0.75\%\) every month. Give your answer correct to the nearest cent, wherever necessary.

a. Calculate the final value of this investment
b. What is the increase in value obtained in part (a) as against investing the same amount for same time at same rate but at simple interest.

$4000 is invested for 3 years at 4%p.a compound interest. If $4000 was invested for 3 years at 4.5% simple interest

i) Which would be the better investment method?

ii) What would be the difference in the final amount? 

$5000 is invested for 4 years at 10% compound interest. What simple rate of interest must be used to give the same final amount at the compound interest rate?

i) $6000 is invested for 30 months, compounding at 1% per month. Find the interest rate earned.

ii) $6000 is invested at a simple interest rate of 1% per month. Find the number of months (1dp) required to earn the same interest as in part (i)