Answer:
a) 13913
b) 4913.82
Step-by-step explanation:
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.
In this question:
Investment of 9000, so [tex]P = 9000[/tex]
Interest rate of 8%, so [tex]r = 0.08[/tex]
Compounded quarterly, so [tex]n = 4[/tex]
5 years and 6 months, that is, 5 years and half, so [tex]t = 5.5[/tex]
(a) How much would the value of her savings at the end of the term?
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(5.5) = 9000(1 + \frac{0.08}{4})^{4*5.5} = 13913.82[/tex]
(b) How much is the interest earned by your savings?
The amount subtracted by the principal. So
13913.82 - 9000 = 4913.82
