4.33333 in simplified fraction form is 4 1/3, and in mathematics a number is considered rational if it can be written as a fraction. So the answer to your question is yes, 4.3333333333............ is a rational number.
The total amount of money which the Stewart family would have to pay into the annuity each quarter is $242.12.
<h3>How to calculate the payment?</h3>
Mathematically, annuity can be calculated by using this formula:
![A = P[\frac{(1+\frac{r}{n} )^{nt} - 1)}{\frac{r}{n} }]](https://tex.z-dn.net/?f=A%20%3D%20P%5B%5Cfrac%7B%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D%20-%201%29%7D%7B%5Cfrac%7Br%7D%7Bn%7D%20%7D%5D)
<u>Given the following data:</u>
- Number of times compounded (quarterly), n = 4.
- Present value, A = $13,000.
- Interest rate, r = 3.6% = 0.036.
Substituting the given parameters into the formula, we have;
![13000 = P[\frac{(1+\frac{0.036}{4} )^{4 \times 11} - 1)}{\frac{0.036}{4} }]\\\\13000 = P[\frac{(1+0.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{(1.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{1.48323960867 - 1}{0.009 }]\\\\13000 = P[\frac{0.48323960867 }{0.009 }]\\\\13000 = 53.6932898522P](https://tex.z-dn.net/?f=13000%20%3D%20P%5B%5Cfrac%7B%281%2B%5Cfrac%7B0.036%7D%7B4%7D%20%29%5E%7B4%20%5Ctimes%2011%7D%20-%201%29%7D%7B%5Cfrac%7B0.036%7D%7B4%7D%20%7D%5D%5C%5C%5C%5C13000%20%3D%20P%5B%5Cfrac%7B%281%2B0.009%20%29%5E%7B44%7D%20-%201%29%7D%7B0.009%20%7D%5D%5C%5C%5C%5C13000%20%3D%20P%5B%5Cfrac%7B%281.009%20%29%5E%7B44%7D%20-%201%29%7D%7B0.009%20%7D%5D%5C%5C%5C%5C13000%20%3D%20P%5B%5Cfrac%7B1.48323960867%20-%201%7D%7B0.009%20%7D%5D%5C%5C%5C%5C13000%20%3D%20P%5B%5Cfrac%7B0.48323960867%20%7D%7B0.009%20%7D%5D%5C%5C%5C%5C13000%20%3D%2053.6932898522P)
P = 13000/53.6932898522
P = $242.12.
Read more on annuity here: brainly.com/question/25792915
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Complete Question:
The Stewart family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 3.6% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money do they need to pay into the annuity each quarter for the annuity to have a total value of $13,000 after 11 years?
228 - 48 = 180
180/48 = 3.75
Its increase 375%
4 is the GCF for these numbers. Hope this helps!
Setting up a ratio
20 ft/7 ft
cannot be reduced ratio is the same as given