Jessica’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 2.6% compounded monthly. Since Jessica and Joe 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.
Jessica
never
rounds her intermediate calculations. She carries out each calculation to as many decimal places as her calculator will indicate. Her calculator displays eight decimal places. She only rounds to the nearest dollar and cents amount at the end of her calculations.
Joe
always
rounds each of his intermediate calculations to 4 decimal places.
Answer each of the following questions separately, showing all your work to reach each answer.
a. How much money will Jessica 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 Jessica’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 Joe calculate to be in the account at the end of 18 years if he rounds at each step to 4 decimal places.
d. With Joe’s calculations, how much
interest
will be earned at the end of 18 years if he rounds at each step to 4 decimal places.