Answer :
Answer:
The exponential function is [tex]A(t) = 1000(1.004)^{12t}[/tex].
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:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
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 [tex]P = 1000, r = 0.048, n = 12[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 1000(1 + \frac{0.048}{12})^{12t}[/tex]
[tex]A(t) = 1000(1 + 0.004)^{12t}[/tex]
[tex]A(t) = 1000(1.004)^{12t}[/tex]
This is the exponential function
How much will you have in your account after 2 years?
This is A(2). So
[tex]A(2) = 1000(1.004)^{24} = 1100.55[/tex]
You will have $1,100.55 in the account after 2 years.