Answer:
[tex]13.54\ 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]A=\$50,000\\ P=\$20,000\\ r=0.07\\n=1[/tex]
substitute in the formula above and solve for t
[tex]\$50,000=\$20,000(1+\frac{0.07}{1})^{t}[/tex]
[tex]2.5=(1.07)^{t}[/tex]
Applying log both sides
[tex]log(2.5)=t*log(1.07)[/tex]
[tex]t=13.54\ years[/tex]
