Answer :

The principal that will grow to $3600 in seven years, eight months at 5.7% compounded annually is $2617.63.

The formula to calculate the future value (FV) of an investment compounded annually is:

[tex]\[ FV = P \times (1 + r)^n \][/tex]

Where:

- [tex]\( FV \)[/tex] = Future Value

- [tex]\( P \)[/tex] = Principal (initial amount)

- [tex]\( r \)[/tex] = Annual interest rate (as a decimal)

- [tex]\( n \)[/tex] = Number of compounding periods

In this case, you're given:

- [tex]\( FV = $3600 \)[/tex]

- [tex]\( r = 5.7\% = 0.057 \)[/tex]

- [tex]\( n = 7 \)[/tex] years and [tex]\( 8 \)[/tex] months, which is equivalent to [tex]\( 7 + \frac{8}{12} \approx 7.67 \)[/tex] years

You need to solve for [tex]\( P \)[/tex]. Rearranging the formula to solve for [tex]\( P \)[/tex]:

[tex]\[ P = \frac{FV}{(1 + r)^n} \][/tex]

Plugging in the values:

[tex]\[ P = \frac{3600}{(1 + 0.057)^{7.67}} \approx 2617.634593 \][/tex]

Rounded to the nearest cent, the principal is $2617.63.

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Complete Question : What is the principal that will grow to $3600 in seven years, eight months at 5.7% compounded annually? The principal is $ (Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

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