Question

First City Bank pays 7.5 percent simple interest on its savings account balances, whereas Second City Bank pays 7.5 percent interest compounded annually. Which bank offers a higher return on savings?

1) First City Bank
2) Second City Bank

Answer 1

Second City Bank offers a higher return on savings compared to First City Bank because its 7.5% interest is compounded annually, meaning the interest each year is calculated on an increased balance including the previously accrued interest, whereas First City Bank's simple interest is always calculated on the original principal only.

Step-by-step explanation:

The student's question involves comparing the return on savings with simple interest versus compounded interest. When First City Bank offers 7.5% simple interest, it means the interest is calculated on the original principal balance only and it's the same amount every year. On the other hand, Second City Bank offers 7.5% interest compounded annually, meaning that the interest for each subsequent year is calculated on the new balance which includes the previous years’ interest.

To illustrate, let's assume you deposit $1,000 into each bank. After one year:

• First City Bank pays you $1,000 x 0.075 = $75
• Second City Bank also pays you $1,000 x 0.075 = $75

After the second year:

• First City Bank again pays $1,000 x 0.075 = $75
• Second City Bank pays ($1,000 + $75) x 0.075 = $80.63

As you can see, the compounded interest from Second City Bank yields a higher amount because it considers the accumulated interest from previous periods. Therefore, Second City Bank offers a higher return on savings compared to First City Bank, which pays simple interest.