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Changing compounding frequency Using annual, semiannual, and quarterly compounding
periods for each of the following, (1) calculate the future value if $5,000 is
deposited initially, and (2) determine the effective annual rate (EAR).
a. At 12% annual interest for 5 years.
b. At 16% annual interest for 6 years.
c. At 20% annual interest for 10 years.

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Jamar Ferry
Jamar FerryLv2
28 Sep 2019

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Changing compounding frequency - Using annual, semiannual, and monthly compounding periods for each of the following, (1) calculate the future value if $3,000 is deposited initially, and (2) determine the effective annual rate (EAR).

a. At 10% annual interest for 4 years.

b. At 14% annual interest for 5 years.

c. At 20% annual interest for 7 years.

Compounding frequency and time value: You plan to invest $2,000 in an individual retirement arrangement (IRA) today at a nominal annual rate of 8%, 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 365-day year), and (4) continuously?

b. What is the effective annual rate (EAR) for each compoundings 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 part a throughc.

Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years, and the credit union pays an annual interest rate of 8%.

a. Determine the future value that Janet will have at the end of 10 years, given that end-of- period deposits are made and no interest is withdrawn, if

(1) $300 is deposited annually and the credit union pays interest annually.

(2) $150 is deposited semiannually and the credit union pays interest semiannually.

(3) $75 is deposited quarterly and the credit union pays interest quarterly.

b. Use your findings in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.

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