Answer:
The amount of money in the account after t years is given by: [tex]A(t) = 5000(1.015)^{4t}[/tex]
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.
Invested $5000 at 6% per year and is compounded quarterly
This means, respectively, that [tex]P = 5000, r = 0.06, n = 4[/tex]
So, the amount of money in the account after t years will be given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 5000(1 + \frac{0.06}{4})^{4t}[/tex]
[tex]A(t) = 5000(1.015)^{4t}[/tex]
