Answer:
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.
[tex]Amount = P(1 + \frac{r}{4})^{4t}[/tex]
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.
[tex]= \frac{5}{100}[/tex]
= 0.05
r = 0.05
t = 1 years
Put in the formula
[tex]Amount = 1000(1 + \frac{0.05}{4})^{4}[/tex]
[tex]Amount = 1000(1 + 0.0125)^{4}[/tex]
[tex]Amount = 1000(1.0125)^{4}[/tex]
[tex]Amount = 1000\times 1.051\ (Approx) [/tex]
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.
[tex]Amount = P(1 + \frac{r}{2})^{2t}[/tex]
As given
Bank B offers 5.1% compounded semiannually .
P = $1000
5.1 % is written in the decimal form.
[tex]= \frac{5.1}{100}[/tex]
= 0.051
r = 0.051
t = 1 years
Put in the formula
[tex]Amount = 1000(1 + \frac{0.051}{2})^{2}[/tex]
[tex]Amount = 1000(1 +0.0255)^{2}[/tex]
[tex]Amount = 1000(1.0255)^{2}[/tex]
[tex]Amount = 1000\times 1.052 (Approx)[/tex]
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 .
Answer:
Bank B by 70.5 cents
Step-by-step explanation:
(AP3X)
