Compound
Interest
Objectives:
- Calculate a periodic rate.
- Determine the number of compounding periods in a given
amount of time.
- Calculate the future value of a compound interest loan.
- Calculate the annual yield of a loan.
- Calculate the present value of a compound interest loan
given its future value.
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Vocabulary:
- compound interest
- compounding period
- periodic rate
- annual yield
- nominal rate
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Formulas:
- Compound Interest Formula:
- Annual Yield Formula:
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Possible
Classroom Examples:
- Find the periodic rate
that corresponds to 12% annual interest compounded
- quarterly
- monthly
- daily
- biweekly
- semi-monthly
- Find the number of periods that corresponds to years if a period is a
- quarter of a year
- month
- day
- Find the future value of $7,300 at 7% compounded annually for 13
years.
- Find the future value
of $12,350 at 6% compounded daily for 10 years.
- Find the annual yield corresponding to
- compounded quarterly
- compounded daily
- Find the present value
that will generate $1000 at 8% compounded annually for 7 years.
- National Trust Savings offers 5-year CDs at 8.25% compounded
daily, and the Bank of the Future offers 5-year CDs at 8.28% compounded
annually. Compute the annual yield for each institution and determine
which is more advantageous for the consumer.
- When Alan Cooper was born, his grandparents deposited $5,000 into
a
special account for Alan’s college education. The account earned 7
¼ % interest compounded daily.
- How much will be in the account when Alan is eighteen?
- If, on becoming eighteen, Alan arranged for the monthly
interest
to be sent to him, how much would he receive each 30-day month?
- David Murtha wants to have an IRA that will be worth $150,000
when he retires at age sixty-five.
- How much must he deposit at age twenty-six at
compounded daily?
- If, at age sixty-five, he arranges for the monthly interest to
be sent to him, how much will he receive each 30-day month?
© 2007 Elizabeth E. K. Jones and the
ASU
Department of
Mathematics and Statistics - All rights reserved.