Consider the interest rate 8% compounded quarterly. 

(a) Find an equivalent interest rate compounded semi-annually. [ /2 ] 

(b) Assume that a principal of $1000 was invested for a year. Show that over the year, both of these interest rates will yield the same future value. [ /2 ] 

(c) Using another concept we have looked at, how else could we determine the answer we got from (a) is equivalent to the given rate? Calculate these values to show they are equivalent.

A loan of $3000 is to be repaid in 3 separate equal payments. The first payment will be 6 months from today, the second will be 9 months from today, and the final payment will be 12 months from today. If interest is accumulated at 2% compounded quarterly, find the payments

A payment of $675 is made 9 months from today to pay off a loan of $1000. Interest will be accrued at 5% compounded quarterly. How much is the second payment made 15 months from today if it pays off the remaining balance?

An account that earns semi-annual interest grew from $2000 to $3000. The effective interest rate for this account is 4.04%. How long (in months) did it take for this growth to occur? Round your number of compounds up to the nearest whole number.