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* Danny wants to earn $500,000 by the time he retires. He puts a huge bonus of $20,000 in an
account. He does not plan on putting any more money in the account. If the account has an
annual interest rate of 11.5%, how long until Danny can retire with $500,000?”

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TaeKwonDoIsDead

Answer:

See Below

Step-by-step explanation:

The question is asking:

After how many years, 20,000 will become 500,000 at an annual interest of 11.5%?

So, we need compound growth formula shown below to solve this:

[tex]F=P(1+r)^t[/tex]

F is future value

P is present amount

r is rate of interest

t is the time of year

Given,

F = 500,000

P = 20,000

r = 11.5% = 11.5/100 = 0.115

t is what we want to find

[tex]F=P(1+r)^t\\500,000=20,000(1+0.115)^t\\25=1.115^t[/tex]

Now, we take natural log of both sides and solve for t:

[tex]Ln(25)=t*Ln(1.115)\\t=\frac{Ln(25)}{Ln(1.115)}\\t=29.57[/tex]

Its is going to take about 29.57 years, rounding, 30 years

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