c What is the average rate of change of the investment from

(c) What is the average rate of change of the investment from the time when the CD is purchased until the time it matures? (Round your answer to two decimal places.)

(f) How much more money would the CD be worth if the interest was compounded continuously instead of periodically? (Assume the minimum amount is invested. Round your answer to two decimal places.)

Solution

Ans(c):

Given amount invested = P = 500
time n= 6 months = 6*30 days = 180 days
rate of interest i= 3.05% yearly = 0.0305/360 daily
Then future value is given by
A=P(1+i)^n=500(1+0.0305/360)^180=507.683109355

Hence average rate of change = 507.683109355-500= 7.683109355
which is approx $7.68

Ans(f):

Given amount invested = P = 500
time n= 6 months = 6/12 year = 0.5 year
rate of interest r= 3.05% yearly = 0.0305
Then future value is given by
A=P*e^(rt)
A=500*e^(0.0305*0.5)=507.683437303

difference amount using previous method of calculation=
507.683437303 - 507.683109355 = 0.000327948000006
Which is almost negligible.