Lia has $1000 to put in a savings account. she is choosing between two banks. bank a offers 5% compounded quarterly and bank b offers 5.1% compounded semiannually. if lia plans on keeping her money in a savings account for a year, which bank would pay her more in interest, and by how much?

The interest given by Bank B is more as compared to the interest given by the Bank A is $1 .

Step-by-step explanation:

Lia has $1000 to put in a savings account. She is choosing between two banks.

First case

Formula for compounded quarterly.

Where P is the principle , r is the rate of interest in the decimal form and t is the time.

As given

Bank A offers 5% compounded quarterly .

P = $1000

5% is written in the decimal form.

= 0.05

r = 0.05

t = 1 years

Put in the formula

Amount = $1051

As

Amount = Principle + Interest

$1051 = $1000 + Interest

Interest = $1051 -  $1000

Interest = $ 51

Thus the Bank A interest is $51.

Second part

Formula for Compounded semiannually.

As given

Bank B offers 5.1% compounded semiannually .

P = $1000

5.1 % is written in the decimal form.

= 0.051

r = 0.051

t = 1 years

Put in the formula

Amount = $1052

As

Amount = Principle + Interest

$1052 = $1000 + Interest

Interest = $1052 - $1000

Interest = $52

Therefore in Bank B interest is $52.

Clearly the interest given by Bank B is more as compared to the interest given by the Bank A.

Thus

More interest  given by the Bank B = Interest given by Bank B-  Interest given by Bank A

Putting the value in the above

More interest  given by the Bank B = $52 - $51

                                                           = $ 1

Therefore the more interest  given by the Bank B than Bank A is $1 .