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.
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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?
10/12
If this isn’t the answer I am truly sorry.
Answer:
y=0.3x - 7.6
Step-by-step explanation:
line: y=ax+b
a= Δy ÷ Δx
a= (-9 + 7) ÷ (-5 - 2)
a= -2 ÷ -7 = approximately 0.3
y=0.3x + b
Now you can fill in one of the points to find b (or both to make sure you got the answer right).
0.3 × 2 + b = -7
0.6 + b = -7
b = -7 - 0.6 = approximately -7.6
So: an equation of the line that passes through this pair of points is y=0.3x - 7.6
On a test, i would write as many decimals as possible if not said not to, to get the most exact answer. Also remember to keep calculating with the number on your calculator and not to round them off for the most exact answer.