(a) Compute the future value of $500 after 5 years if it earns an annual interest rate of 6% compounded quarterly.

(b)Determine the monthly compounding interest rate that would cause $400 to grow to $644.89 in four years.

(c)A 20-year-old student saves $10 a day for her retirement. Every day she places $10 in a drawer. At the end of each year, she invests the accumulated savings ($3,650) into a brokerage account with an expected annual return of 8%. The last investment she will make is at the age of 64.

i. If she keeps saving in this manner, how much will she accumulate at the age of 64?

ii. If a 40-year-old investor also begins saving in the same manner, how much would he have at the age of 65?

iii. How much would the 40-year-old investor have to save each year to accumulate the same amount at the age of 65 as the 20-year-old student?

(d) Determine the value of the following cash flows at the end of year 4 with an annual interest rate of 8% compounded quarterly.