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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.

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Lelia Lubowitz
Lelia LubowitzLv2
28 Sep 2019

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Related questions

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.

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.

Problem 1: $3,000 is invested at 7.2% interest. Find the total amount (A) at the end of 5 years if:
a.) Simple interest is earned. (see the "Simple Interest Example" tab)
b.) Interest is compounded annually (see the "Compound Interest Illustration" tab)
c.) Interest is compounded quarterly (see the "Other Compounding Periods" tab)
d.) Interest is compounded monthly (see the "Other Compounding Periods" tab)
Problem 2: A department store charges 12% interest on the unpaid balance of customer charge accounts.
A customer owes $135, and the bill goes unpaid for 4 months. How much will the customer have to
repay after 4 months? Interest is compounded monthly (note that the 12% is an annual rate). (see the "Other Compounding Periods" tab)
Problem 3: A typical family of four spends approximately $600 per month for food. Food costs are
predicted to rise by 4.8% per year for the next 5 years. In five years, how much should
the family budget per month for food? Treat this as compound annual growth. (see the "Compound Interest Illustration" tab)
(assume annual compounding)
Problem 4a: A couple plans to begin saving money for a down payment toward the purchase of a home.
They plan to purchase a home 4 years from now. Right now, home prices are predicted
to rise by 5% per year for the next 5 years. If this prediction is accurate, how much
can this couple expect to pay in 4 years for a home that is currently valued at $210,000?
(what will be the total sales price in 4 years of a home worth $210,000 today?) (see the "Compound Interest Illustration" tab)
Problem 4b: The couple wants to have a 20% down payment on the purchase price in 4 years. Suppose they
have found a mutual fund that earns an average of 8% per year. How much should they invest in the
mutual fund today in order to have enough for a down payment in 4 years?
Assume annual compounding.
(Find the down payment first - that will be their "A" or future value of what they will invest)
(see the "Other Problem Types" tab - we are trying to find the principal or present value to be invested to grow to the down payment amount)
Problem 5: An electric company predicts that the cost of electricity will rise at the rate of 2% per
year for the next ten years. If the average monthly electricity for consumers in this area
is $225, predict the monthly amount that consumers can expect to pay 10 years from now.
(see the "Compound Interest Illustration" tab)

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