Answer:
See explanation
Step-by-step explanation:
The question is incomplete as the invested amount and the interest rate are not given. However, I will give a general method of solving it.
Assume that:
[tex]r = 5\%[/tex] --- interest rate
[tex]PV =9000[/tex] --- Present value or invested amount
To calculate time (in years), we make use of the following formula of future value
[tex]FV = PV(1 + r)^n[/tex]
Where
[tex]FV = 11800[/tex]
So:
[tex]11800 = 9000( 1 + 5\%)^n[/tex]
Divide both sides by 9000
[tex]1.31 = ( 1 + 5\%)^n[/tex]
Take logarithm of both sides
[tex]Log(1.31) = Log(1 + 5\%)^n[/tex]
Apply law of logarithm
[tex]Log(1.31) = nLog(1 + 5\%)[/tex]
Make n the subject
[tex]n = \frac{Log(1.31)}{Log(1 + 5\%)}[/tex]
Express 5% as decimal
[tex]n = \frac{Log(1.31)}{Log(1 + 0.05)}[/tex]
[tex]n = \frac{Log(1.31)}{Log(1.05)}[/tex]
[tex]n = \frac{0.1173}{0.0212}[/tex]
[tex]n \approx 6[/tex]
The time to reach the future value is approximately 6 years.
Use the above explanation to answer your question
