Question

find the amount in an account after years if invested$5000 at 6% per year and is compounded quarterly​

Answer 1

Answer:

The amount of money in the account after t years is given by: $A(t) = 5000(1.015)^{4t}$

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.

Invested $5000 at 6% per year and is compounded quarterly​

This means, respectively, that $P = 5000, r = 0.06, n = 4$

So, the amount of money in the account after t years will be given by:

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

$A(t) = 5000(1 + \frac{0.06}{4})^{4t}$

$A(t) = 5000(1.015)^{4t}$