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>
Kate paid $25.39 for her purchases.
Kate will receive $24.61 in change.
Step-by-step explanation:
Given,
Cost of t-shirt = $12.95
Cost of pair of shorts = $10.95
Total = cost of t-shirt + cost of pair of shorts
Total = 12.95 + 10.95 = $23.90
Sales tax = 6.25% of total amount
Amount of sales tax = 
Amount of sales tax= $1.49
Total amount with sales tax = 23.90 + 1.49 = $25.39
Kate paid $25.39 for her purchases.
Amount paid = $50
Change received = Amount paid - Bill amount
Change received = 50 - 25.39 = $24.61
Kate will receive $24.61 in change.
Keywords: sales tax, addition
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The answer is 3n-4 because 4 is being subtracted
Well if those are the only 3 options of a segment, then there is a 1/3 chance of landing on A, then a 1/3 chance of landing on B, then a 1/3 chance of landing on C. Multiply the fractions together to get 1/27. However that isn't one of your answers. I'm thinking that the spinner has 4 sections, meaning 1/4 chance of A, then 1/4 chance of B, then 1/4 chance of C. Multiply these together to get 1/64, which is one of your answers. That's my input anyway
