Answer:
The retirement fund will last for 33 years and 7 months
Explanation:
We need to solve for time in an ordinary annuity
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C $15,000.00
rate 0.004 (4.8% divide by 12 month)
PV $3,000,000
time n
[tex]15,000 \times \frac{1-(1+0.004)^{-n} }{0.004} = 3,000,000\\[/tex]
we clear for n as much as we can and solve
[tex](1+0.004)^{-n}= 1-\frac{3,000,000\times0.004}{15,000}[/tex]
[tex](1+0.004)^{-n}= 0.20[/tex]
now we use logarithmic properties to solve for n:
[tex]-n= \frac{log0.2}{log(1+0.004)[/tex]
-403.16
this will be a value in months so we divide by 12 to get it annually
403/12 = 33,5833
we convert the residual to months:
0.5833 x 12 = 6.996 = 7 months
