Given:
P = $5338.18, principal
r = 5.9% = 0.059, interest rate
n = 2, nuber of compoundings per year
t = duraton, years
A = $10,000, target value.
Use the formula
[tex]P(1 + \frac{r}{n})^{nt} = A [/tex]
That is,
[tex]5338.18(1 + \frac{0.59}{2})^{2t} =10000\\1.0295^{2t}=1.8773 [/tex]
[tex]t = \frac{1}{2} ( \frac{ln(1.8773)}{ln(1.0295)} )=10.832\, yrs\,=10yrs,\,10\,mo[/tex]
Answer: 10years, 10 months
