Question

111. Dani has $1,000 in an investment account that earns 3% per year, compounded monthly.

Answer 1

Answer:

$A(t) = 1000(1.0025)^{12t}$

Step-by-step explanation:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money in the account after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the number of years the money is invested or borrowed for.

For this problem, we have that:

$P = 1000$

The investment is compounded monthly. There are 12 months in a year. So $n = 12$

The interest rate is 3%. So $r = 0.03$.

So

The amount of money in her account after t years is:

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(t) = 1000(1 + \frac{0.03}{12})^{12t}$

$A(t) = 1000(1.0025)^{12t}$