Part 1:

John and Sarah decide to save for retirement with an annuity.

John has found an annuity that pays 1.75 % compounded monthly.Provided the couple deposited $250 each month.

Answer the following questions separately, showing the formula and all of your work used to reach your answers.

What would be the total value of their annuity at the end of 30 years provided the interest rate remains the same?

How much money in interest will the couple have earned?

Sarah found an annuity that pays 2.25 % compounded semi-annually.Provided the couple made a $1,500 deposit every six months;

What would be the total value of this annuity at the end of 30 years provided the interest rate remains the same?

How much money in interest will the couple have earned?

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Part 2:

John's parents will set up a savings account for their first grandchild. They saved $12,000 to invest and they have identified an account paying 2.5 % compounded monthly.Since John and Sarah just finished a consumer mathematics course, they each decide to calculate how much the account will grow and how much interest earned at the end of 18 years.

John never rounds his intermediate calculations. He carries out each calculation to as many decimal places as the calculator will indicate. His calculator displays eight decimal places, and he only rounds to the nearest dollar and cents amount at the end of his calculations.

Sarah always rounds each of her intermediate calculations to 4 decimal places.

Answer the following questions separately, showing the formula and all of your work used to reach your answers.

How much money will John calculate to be in the account at the end of 18 years if he uses the calculator which answers out to 8 decimal places?

Using John's calculations, how much interest will be earned at the end of 18 years provided he uses a calculator that answers out to 8 decimal places?

How much money will Sarah calculate to be in the account at the end of 18 years provided she rounds at each step to 4 decimal places?

Using Sarah's calculations, how much interest will be earned at the end of 18 years provided she rounds at each step to 4 decimal places?