Answer :
Answer:
[tex]t=2.25\ years[/tex]
Step-by-step explanation:
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=?\ years\\ P=\$7,000\\ r=0.034\\n=4\\A=\$7,553[/tex]
substitute in the formula above
[tex]7,553=7,000(1+\frac{0.034}{4})^{4t}[/tex]
solve for t
[tex](7,553/7,000)=(1.0085)^{4t}[/tex]
[tex](1.079)=(1.0085)^{4t}[/tex]
Applying log both sides
[tex]log(1.079)=log[(1.0085)^{4t}][/tex]
[tex]log(1.079)=(4t)log(1.0085)[/tex]
[tex]t=log(1.079)=[(4)log(1.0085)][/tex]
[tex]t=2.25\ years[/tex]