To solve this we are going to use the future value of annuity due formula:
![FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%2AP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bkt%7D-1%20%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where
is the future value
is the periodic deposit
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the number of deposits per year
We know for our problem that
and
. To convert the interest rate to decimal form, we are going to divide the rate by 100%:
. Since Ruben makes the deposits every 6 months,
. The interest is compounded semiannually, so 2 times per year; therefore,
.
Lets replace the values in our formula:
![FV=(1+ \frac{0.1}{2} )*420[ \frac{(1+ \frac{0.1}{2})^{(2)(15)}-1 }{ \frac{01}{2} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7B0.1%7D%7B2%7D%20%29%2A420%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.1%7D%7B2%7D%29%5E%7B%282%29%2815%29%7D-1%20%7D%7B%20%5Cfrac%7B01%7D%7B2%7D%20%7D%20%5D)
We can conclude that the correct answer is <span>
$29,299.53</span>
Answer:
48
Step-by-step explanation:
x/8+3=9
x/8=9-3
x/8=6
x=6*8
x=48
Yes you can assume they are similar because the sides that correspond with one another are half of the big triangles measurements. 16/2=8 12/2=6 etc.
Answer:
Length = 15 cm, width = 12 cm, Perimeter = 54 cm
Step-by-step explanation:
The ratio of the length and breadth of a rectangle is 5:4 and its area is 180 cm².
Length = 5x
Breadth = 4x
Area of rectagle,
A = bl
180 = 5x × 4x
180 = 20x²
x² = 9
x = 3
Length = 5x = 5(3) = 15 cm
Width = 4x = 4(3) = 12 cm
Perimeter of rectangel,
P = 2(l+b)
= 2(15+12)
= 54 cm
Hence, this is the required solution.
Answer:
AB would be 18 or the first choice.
Since BD is the median that means from A to D and from D to C are equal. We set this up as an equation and solve it.
<em>x + 8 = 2x - 17</em>
<em> </em><em><u>+ 17 +17</u></em>
<em>x + 25 = 2x</em>
<em><u>-x -x</u></em>
<em> 25 = x</em>
This gives us our first bit of the answer. Then we plug this into our equation for the length of AB to get 18.
Step-by-step explanation:
hope this helps. . . <3
good luck! uωu
