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:
75 %
Step-by-step explanation:
To solve for the above question,
The percentage of pupils that submitted their project on time
= Number of pupils that submitted their project on time/Number of pupils × 100
Number of pupils that submitted their project on time = 30 pupils
Number of pupils = 40 pupils
= 30/40 × 100
= 75 %
The percent of the pupils that submitted their project on time is 75%
Answer:
13
Step-by-step explanation:
a parallelogram has sides that are parallel to the opposite side. This means that y + 7 is going to be parallel to 20.
Two opposing sides of a parallelogram are parallel and equal
You know that the length of both of the sides is equivalent because the other set of opposing lines is also parallel (you can think of it as cutting off the line segment of y+7 and 20 at the same length. )
this means that we can set up the equation to find y as:
y + 7 = 20
then, you can proceed to find y by isolating it:
y + 7 = 20 ; so therefore
y + 7 = 20
- 7 -7
y = 13
y = 13
So, the value of y is 13
Answer:
y = -8
Step-by-step explanation:
The domain is the x values so x=-3
y = x-5
Substituting x=-3
y = -3-5
y=-8
Answer: =-2(xy-6y-5)
Step-by-step explanation: multiply -(2xy-6 x 2y+ 4 x 2 -6 x 3) remove the parenthesis -2xy + 12 y - 8 +18 calculate -2xy+12y-8+18 factor the expression -2xy + 12y + 10 solution -2 (xy- 6y-5)
