Answer:
11 years
Explanation:
The computation of the number of years that should be taken is shown below:
As we know that
A = P(1 + r%)^n
here
A = future value
P = present value
r = rate of interest
n = time period.
So, the future value of $33,556.25 is
= $33,556.25× (1.12)^n
In addition to this,
The Future value of the annuity is
= Annuity[(1+rate)^time period-1] ÷ rate
= $5,000 [(1.12)^n-1] ÷ 0.12
Now
$220,000 = $33,556.25 × (1.12)^n + $5,000[(1.12)^n-1] ÷ 0.12
$220,000 = $33,556.25 × (1.12)^n + $41,666.67[(1.12)^n-1]
$220,000 = $33,556.25 × (1.12)^n + $41,666.67 × (1.12)^n - $41,666.67
($220,000 + $41,666.67) = (1.12)^n[$33,556.25 + $41,666.67]
(1.12)^n = ($220,000 + $41,666.67) ÷ ($33,556.25 + $41,666.67)
(1.12)^n = $3.478549866
Now take the log to the both sides
n × log 1.12 = log 3.478549866
n = log 3.478549866 ÷ log 1.12
= 11 years
