Answer:
60.2 years.
Explanation:
Initial deposit (P) = $10,000
Frequency of compounding = semi annual
Annual rate of return = 9%
Therefore, semi-annual rate of return (r) = 9%/2 = 4.5%
Target sum (A) = $2,000,000
Accordingly, using the compounding interest formula,
[tex]P(1+r)^{n} = A[/tex]
= [tex]10,000(1+0.045)^{n} = 2,000,000[/tex]
= [tex]10,000(1.045)^{n} = 2,000,000[/tex]
= [tex]1.045^{n} = \frac{2,000,000}{10,000}[/tex]
= [tex]1.045^{n} = 200[/tex]
By interpolation, the value of n that satisfies the equation is 120.4.
Thus, the target amount will be achieved in 120.4 semi-annual periods, same as (120.4/2) = 60.2 years.
