Answer:
Part 1) [tex]I=\$2,693.12[/tex]
Part 2) [tex]A=\$7,693.12[/tex]
Step-by-step explanation:
Part 1) What is the amount of interest this account will earn in 5 years?
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=5\ years\\ P=\$5,000\\ r=9\%=9/100=0.09\\n=1[/tex]
substitute in the formula above
[tex]A=5,000(1+\frac{0.09}{1})^{1*5}[/tex]
[tex]A=5,000(1.09)^{5}[/tex]
[tex]A=\$7,693.12[/tex]
Remember that the interest is equal to
[tex]I=A-P[/tex]
substitute
[tex]I=\$7,693.12-\$5,000=\$2,693.12[/tex]
Part 2) What is the amount in the account?
The amount in the account after 5 years is equal to
[tex]A=\$7,693.12[/tex] ----> see part 1)
