Question

$650 is invested in an account earning 8.6% interest (APR), compounded monthly. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

Answer 1

Answer:

The value of the acount after t years is of $A(t) = 650(1.0072)^{12t}$

The annual growth rate is of 0.72%.

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.

$650 is invested in an account earning 8.6% interest (APR), compounded monthly.

This means that $P = 650, r = 0.086, n = 12$. So

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

$A(t) = 650(1 + \frac{0.086}{12})^{12t}$

$A(t) = 650(1.0072)^{12t}$

The value of the acount after t years is of $A(t) = 650(1.0072)^{12t}$

Annual growth rate

1.0072 - 1 = 0.0072 = 0.72%

The annual growth rate is of 0.72%.