Answer:
Approx 37 years.
Step-by-step explanation:
The compound interest formula is :
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Here, A = $50000
P = $5000
r = 6.5% or 0.065
n = 1
t = ?
Putting these values in formula we get;
[tex]50000=5000(1+\frac{0.065}{1})^{1t}[/tex]
=> [tex]50000=5000(1.065)^{t}[/tex]
=> [tex]10=(1.065)^{t}[/tex]
Taking log on both sides;
[tex]ln(10)=ln(1.065)^t[/tex]
=> [tex]t=\frac{ln(10)}{ln(1.065)}[/tex]
We get t = 36.56 rounding to 37 years.
