Accounting-Assume that a pension plans offers to pay $300,000

| January 30, 2017

Question
I am unsure when an interest rate is considered an EAR vs and APR. My teacher gave us two questions and in one case an EAR is used and the other an APR is used however, in both cases the wording is the exact same. Here are the questions:

1. Assume that a pension plans offers to pay $300,000 on a person’s retirement (his/her sixty-fifth birthday) or a semi annual annuity for the remainder of the person’s life- i.e starting 6 months from the date of retirement and including his/her date of death. INTEREST RATES ARE 8 PERCENT COMPOUNDED SEMI ANNUALLY,and a person’s life expectancy has been determined statistically as being 80 year. Calculate the amount of annuity that would make a person indifferent between the options.

2. Laura Smith is planning for her and her husband Luke’s retirement. Both Luke and Laura expect to retire in 35 years (when they turn 65). The life expectancy of men is 75 years and the life expectancy of women is 85 years (i.e., assume that they die the day before their 75th or 85th birthday). During retirement (while they are living), the couple wants to withdraw $10,000 at the beginning of each year from their savings account- $5,000 for each of them. Assume that the interest rate during their retirement is 10 percent compounded annually; the interest rate after Luke dies is 12% compounded semi- annually; and, the interest rate prior to retirement is 9 percent compounded annually.How much will they have to deposit in their joint savings account each month (beginning one month from now and ending on their retirement date)?

I know the answers to the question so that is not what I am asking. I am wondering why is question 1 the interest rate is an APR and why is question 2, the interest rates that i bolded are calculated as EARs.

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