Question

suppose you deposit $1000 in a savings account that pays 4.8% interest compounded monthly. Write an exponential function to model the amount of money in your savings account. How much will you have in your account after 2 years?

Answer 1

Answer:

The exponential function is $A(t) = 1000(1.004)^{12t}$.

You will have $1,100.55 in the account after 2 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money 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 year and t is the time in years for which the money is invested or borrowed.

Deposit $1000 in a savings account that pays 4.8% interest compounded monthly.

This means that $P = 1000, r = 0.048, n = 12$. So

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

$A(t) = 1000(1 + \frac{0.048}{12})^{12t}$

$A(t) = 1000(1 + 0.004)^{12t}$

$A(t) = 1000(1.004)^{12t}$

This is the exponential function

How much will you have in your account after 2 years?

This is A(2). So

$A(2) = 1000(1.004)^{24} = 1100.55$

You will have $1,100.55 in the account after 2 years.