Please answer 5,6,7. With explanation.

Mathematics

1 answer:

Anestetic [448]3 years ago

8 0

First you need to know some rules 2 numbers that are the same with coefficients divided : you differentiate those coeff
and multyplied :you sum up them

12x^8/3x^3= 4x^8-3=4x^5

20^2x=20^x*20^x

m^5*m^-7=m^5-7=m^-2

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How much should a family deposit at the end of every 6 months in order to have $4000 at the end of 3 years? The account pays 5.9

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We are asked to determine the present value of an annuity that is paid at the end of each period. Therefore, we need to use the formula for present value ordinary, which is:

$PV_{ord}=C(\frac{1-(1+i)^{-kn}}{\frac{i}{k}})$

Where:

$\begin{gathered} C=\text{ payments each period} \\ i=\text{ interest rate} \\ n=\text{ number of periods} \\ k=\text{ number of times the interest is compounded} \end{gathered}$

Since the interest is compounded semi-annually this means that it is compounded 2 times a year, therefore, k = 2. Now we need to convert the interest rate into decimal form. To do that we will divide the interest rate by 100: