Question

The function f(x) = 2,500(1 + 0.021/365)365t models the balance in a savings account. Which statement accurately describes the account?
A.
The account had an initial balance of $2,500 and compounds monthly at an annual interest rate of 2.1%.
B.
The account had an initial balance of $2,500 and compounds yearly at an annual interest rate of 2.1%.
C.
The account had an initial balance of $2,500 and compounds daily at an annual interest rate of 0.21%.
D.
The account had an initial balance of $2,500 and compounds daily at an annual interest rate of 2.1%.

Answer 1

Answer:

D

Step-by-step explanation:

If we look at the formula for compound growth and learn what each variable represents, we can solve this problem very easily.

The formula is:

Compound Growth >>  $F=P(1+\frac{r}{n})^{nt}$

Where

F is the Future Amount (accumulated amount after certain years)

P is the Initial Balance (principal amount)

r is the rate of interest (given in decimal)

n is the number of compounding (if 2, compounded semi annually, 4 means compounded quarterly, 52 means compounded weekly, and 365 means compounded daily)

t is the time in years

Now, the formula given is:

$f(x)=2500(1+\frac{0.021}{365})^{365t}$

Comparing this with compound growth formula, we see that:

• 2500 is the initial balance
• 0.021 * 100 = 2.1% is the interest rate
• n = 365 means compounded daily

Now, looking at the answer choices, we see that D is the correct choice.