Question

hey can u pls answer this question i am really stuck I will award brainliest for the first correct answer

Answer 1

Answer for the first box = 6000

Answer for the second box = 1.004

Answer for the third box = 720

So the full equation is $C(t) = 6000(1.004)^{12t} + 720t$

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Explanation:

The compound interest formula is

A = P( 1+r/n )^(n*t)

where

• P = amount deposited (principal)
• r = interest rate in decimal form
• n = number of times we compound per year (compounding frequency)
• t = number of years

In this case,

• P = 6000
• r = 4.2% = 4.2/100 = 0.042
• n = 12 since there are 12 months in a year (it explains the 12 in the exponent in the answer)
• t = unknown, we leave this as is

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

$b(t) = 6000(1.004)^{12t}$ = amount in savings account after t years go by

$h(t) = 720t$ = amount in safe after t years

leading to

$C(t) = b(t) + h(t) = 6000(1.004)^{12t} + 720t$