Answer for the first box = 6000
Answer for the second box = 1.004
Answer for the third box = 720
So the full equation is [tex]C(t) = 6000(1.004)^{12t} + 720t[/tex]
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Explanation:
The compound interest formula is
A = P( 1+r/n )^(n*t)
where
In this case,
So we go from this
A = P( 1+r/n )^(n*t)
to this
A = 6000( 1+0.042/12 )^(12t)
A = 6000(1.0035)^(12t)
A = 6000(1.004)^(12t)
The 1.0035 rounded to 1.004 when rounding to three decimal places, as the instructions mention.
So far we only considered the amount placed into the bank. But there's also the amount placed in the safe at home. We have $60 placed in here per month. This is 60*12 = 720 dollars per year. If t years go by, then a total of 720t dollars is put in the safe.
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So in summary we found
[tex]b(t) = 6000(1.004)^{12t}[/tex] = amount in savings account after t years go by
[tex]h(t) = 720t[/tex] = amount in safe after t years
leading to
[tex]C(t) = b(t) + h(t) = 6000(1.004)^{12t} + 720t[/tex]
