Respuesta :

danikakuliko

To begin, we know that the formula for annual compound interest, including principal sum, is: A = P (1 + r/n)^(nt)

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for


So plugging in the information you have we get this equation:

1000 = P (1 + 0.06/2)^(2)(5)

then the rest is basic math. *make sure to always follow PEMDAS*

divide then add what is in the paranthesis: (0.06/2)+1 = 1.03

then multiply 2*10 to get the exponent to 10

1000=P(1.03)^10

next step we raise 1.03 to the 10th power

1000=P(1.3439)

Last but not least, to isolate the principal, we divide 1.3439 to the other side.

1000/1.3439

since we are finding a dollar amount, round to the hundredths place

The answer is D. $744.09

hope this helps! :)

mreijepatmat
Compound interest formula: A=P(1+i%)ⁿ , where:

 A = final amount, P= initial amount, i%, the YEARLY interest and n= # years or the PERIOD.
If the interest is reckoned twice a year (every 6 months), then the yearly interest should be divided by 2, but at the same time the period (no longer 1 year)  is to be multiplied by 2:

Then  A = P(1 + I%/period)^(n x period)

1000 = P(1 + 6%/2)⁵ˣ²

1000 = P(1+3%)¹⁰

1000 = P(1.03.)¹⁰

1000 = P(1.343916)   and P = 1000/1.343916

P = $744.09

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