Question

Joanna will deposit $1,530 in an account that earns 6% simple interest every year. Her sister Zinaya will deposit $1,500 in an account that earns 8% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which statement about the balances of Joanna's accounts and Zinaya's accounts at the end of the 3 years is true? Who has more money in her account?

Options:
A) Joanna's account will have about $5.40 more than Zinaya's account.
B) Zinaya's account will have about $5.40 more than Joanna's account.
C) Joanna and Zinaya will have the same amount of money in their accounts.
D) The question does not provide enough information to determine the difference in their account balances.

Answer 1

After calculating the future value of Joanna's simple interest account and Zinaya's compound interest account, it is determined that Zinaya's account will have more money after 3 years. Zinaya's balance will be approximately $1,889.568, whereas Joanna's will be $1,803.4, making option B) the correct answer.

Step-by-step explanation:

To determine who will have more money after 3 years, we need to calculate the future value of each account using the given interest rates and the fact that one is compounded annually while the other is simple interest. For Joanna's account with simple interest, the future value can be calculated as follows:

Future Value = Principal + (Principal × interest rate × time)

For Joanna:
Future Value = $1,530 + ($1,530 × 0.06 × 3)
Future Value = $1,530 + $273.4
Future Value = $1,803.4

For Zinaya's account, we use the formula for compound interest:

Future Value = Principal × (1 + interest rate)^n

Where n is the number of times interest is compounded. Since it's compounded annually, n is 3 for the 3 years.

For Zinaya:
Future Value = $1,500 × (1 + 0.08)^3
Future Value = $1,500 × (1.08)^3
Future Value = $1,500 × 1.259712
Future Value = $1,889.568

Comparing the two amounts, Zinaya's account will have $1,889.568 while Joanna's account will have $1,803.4. Therefore, Zinaya's account will have more money after 3 years.

The correct statement is option B): Zinaya's account will have about $5.40 more than Joanna's account. This is true if we round Zinaya's account balance ($1,889.568) to the nearest dollar.