$(6$ marks$)$

b$.$ Amia is planning for her retirement and wants to invest $K200,000$ into a fund that will provide her with annual payments over $10$ years. The fund offers an interest rate of $8\%$ per year. She also wants to know the future value of her investments if she decides to reinvest at the same rate.

Required:

i$.$ If Amia reinvests $K200,000$ for $10$ years at an $8\%$ annual interest rate, what will be the future value of her investment at the end of the period?

ii$.$ What would be the future value of an annuity where Amia deposits K$20,000$ annually into an account earning $8\%$ interest for the next $10$ years?

$(6$ marks$)$