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1) Maria’s parents tell them that they will set up a savings account

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1) Maria’s parents tell them that they will set up a savings account
for their first grandchild. They have $15,000 to invest and have identified an account that pays 2.75% compounded monthly. Since Maria and John both just finished a course on consumer mathematics, they each decide to calculate how much the account will have in it and the interest earned at the end of 18 years.

Maria never rounds her intermediate calculations. She carries out each calculation to as many decimal places as her calculator will indicate. She only rounds to the nearest dollar and cents amount at the end of her calculations.

John always rounds each of his intermediate calculations to 4 decimal places.

Answer each of the following questions separately

a. How much money will Maria calculate to be in the account at the end of 18 years if she uses a calculator that gives answers out to 8 decimal places?

b. With Maria’s calculations, how much interest will be earned at the end of 18 years if she uses a calculator that gives answers out to 8 decimal places?

c. How much money will John calculate to be in the account at the end of 18 years if he rounds at each step to 4 decimal places.

d. With John’s calculations, how much interest will be earned at the end of 18 years if he rounds at each step to 4 decimal places.

(2) Maria and John decide to save for retirement with an annuity.

Answer each of the following questions separately

A. Maria has found an annuity that pays 1.5% compounded monthly. If they made a deposit of $200 each month,

a. what would be the total value of this annuity at the end of 30 years if interest rate remains the same?

b. how much interest will they have earned?

B. John has found an annuity that pays 2.5% compounded semi-annually. If they made a deposit of $1200 every six months,

a. what would be the total value of this annuity at the end of 30 years if interest rate remains the same?

b. how much interest will they have earned?

 
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