Question

?You plan to invest ?$2,100 in an individual retirement arrangement? (IRA) today at a nominal annual rate of 88?%, which is expected to apply to all future years.

a. How much will you have in the account at the end of 10 years if interest is compounded? (1) annually,? (2) semiannually,? (3) daily? (assume a? 365-day year), and? (4) continuously?

b. What is the effective annual? rate, EAR, for each compounding period in part a??

c. How much greater will your IRA balance be at the end of 10 years if interest is compounded continuously rather than? annually?

d. How does the compounding frequency affect the future value and effective annual rate for a given? deposit? Explain in terms of your findings in parts a through c.

Answer 1

I think there is a typo in annual rate..Assuming nominal annaul rate to be 8% and not 88%

a. How much will you have in the account at the end of 10 years if interest is compounded?

(1) annually

=2100*(1+8%)^10=4533.742494

(2) semiannually

=2100*(1+8%/2)^20=4601.3586

?(3) daily?

=2100*(1+8%/365)^3650=4673.226284

(4) continuously

=2100*e^(0.08*10)=4673.63595

b. What is the effective annual? rate, EAR, for each compounding period in part a??

(1) annually

=8%

(2) semiannually

=(1+8%/2)^2-1=8.16%

?(3) daily?

=(1+8%/365)^365-1=8.3277572%

(4) continuously

=e^(0.08)-1=8.3287068%

c. How much greater will your IRA balance be at the end of 10 years if interest is compounded continuously rather than? annually?

=4673.63595-4533.742494=139.893456

d. How does the compounding frequency affect the future value and effective annual rate for a given? deposit? Explain in terms of your findings in parts a through c.

Compounding frequency increases the future value and EAR increases