Answer:
Step-by-step explanation:
The formula you need for this is
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]
where A(t) is the final amount after the compounding is done, P is the initial investment, r is the interest rate in decimal form, n is the number of times per year that the money is compounded, and t is the time in years. Filling in accordingly:
[tex]1708=1170(1+\frac{r}{4})^{(4)(6)}[/tex]
First things first. Simplify by division and then multiply the n by the t to get the exponent:
Divide 1708 by 1170 to get the equation:
[tex]1.45982906=(1+\frac{r}{4})^{24}[/tex]
Undo the 24th power by taking the 24th root of both sides to get:
[tex]1.015888202=1+\frac{r}{4}[/tex] Now subtract 1 from both sides to get
[tex].0158882024=\frac{r}{4}[/tex] Multiply both sides by 4 to finish it off and get that
r = .0635528 but since we want the percentage, we move the decimal 2 places to the right and round to r = 6.4% which is choice A.
