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    Calculating EAR, APR, Effective Interest Rate, Retirement Saving

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    1) Your savings account offers monthly compounding. If your money doubles in 5 years what is the EAR and APR on the account?

    2) The Jet Co. has an $80,000 line of credit with a 12% interest rate and a 10% compensating balance requirement which is based on the total amount borrowed. What is the effective annual interest rate if the firm needs $45,000 of cash for one year?

    3) You are saving for your retirement in 20 years. You hope to have an annual income of $80,000 per year (at the beginning of each year). At retirement you will have a life expectancy of 25 years and when you die you plan to leave $100,000 to your Community Foundation Fund. Upon retirement, all of your funds will earn a 7% EAR.

    You have a defined contribution retirement plan in which your employer invests $1,000 per month. The account pays a 9% APR with monthly compounding. The balance of your retirement savings will come from your annual (end of year) contributions into an investment account that pays an 11% EAR.

    How much money do you need when you retire in 30 years?

    How much do you need to set aside each year to meet your retirement goal?

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    Solution Preview

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    Time 5 years
    Term monthly compounding
    # of compounding period 12 per year
    60 total
    Interest 100% at the end of 5 years

    Monthly Annual
    EAR 1.24% 14.87%
    APR 1.16% 13.94%

    1. Compute monthly APR
    2. Multiply monthly APR by 12 to get annual APR.
    3. Compute annual EAR from annual APR
    4. ...

    Solution Summary

    The solution examines EAR, APR, effective interest rates and retirement savings calculations.