d$.$ Nuhu is evaluating different investment options and wants to understand how the interest rate affects the growth of his savings. He is considering two options: one with annual compounding and another with quarterly compounding. He is also looking at the time it will take for his investment to double at a given interest rate.

Required:

i$.$ Nuhu invests in a savings account offering a nominal interest rate of $8\%$ compounded quarterly. What is the effective annual rate $($EAR$)$ for this investment?

ii$.$ If Nuhu wants his $K10,000$ investment to double at an $8\%$ annual interest rate, how many years will it take for the investment to reach $K20,000?$

iii. Nuhu is considering a $5-$year investment and wants to determine the interest rate required to grow his $K15,000$ to $K20,000.$ What is the required interest rate?

$(6,$ marks$)$