Answer:
Bank B because the more often you compound interest, the more interest you earn.
Step-by-step explanation:
Bank A compounds the interest once a year.
Bank B compounds the interest twice a year.
Let's create an example of two investments of the same amount of money, the same interest rate, and the same time. The only difference will be the number of times the interest is compounded per year.
Compound interest formula:
[tex] A = P(1 + \dfrac{r}{n})^{nt} [/tex]
where
A = future value
P = principal invested
r = interest rate
t = number of years
n = number of times interested is compounded in 1 year
Example:
P = $1000
r = 5%
t = 5 years
Bank A: n = 1
Bank B: n = 2
Bank A:
[tex] A = $1000(1 + \dfrac{0.05}{1})^{1 \times 5} = $1276.28[/tex]
Bank B:
[tex] A = $1000(1 + \dfrac{0.05}{2})^{2 \times 5} = $1280.08[/tex]
Bank A's investment is worth $1276.28 after 5 years, but Bank B's investment is worth $1280.08 after the same 5 years. Compounding twice per year instead of only once per year earns more interest.
