For the given question, the summation that represents the money in account is:
![\begin{aligned}\sum_{10}^{n=1}316.5(1.055)^{n-1} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csum_%7B10%7D%5E%7Bn%3D1%7D316.5%281.055%29%5E%7Bn-1%7D%20%5Cend%7Baligned%7D)
The principal amount if compounded annually, the formula that represents the amount to be received after n years is:
where A is the amount received after compounding, P is the principal, r is the rate of interest and t is the tenure.
<h3>Solution:</h3>
Given:
Annual interest rate(r) is 5.5%
Principal is(P) $300
Tenure is(t) 10 years
On substituting the values in the formula ![\rm A = P(1 + \dfrac{r}{100})^t](https://tex.z-dn.net/?f=%20%5Crm%20A%20%3D%20P%281%20%2B%20%5Cdfrac%7Br%7D%7B100%7D%29%5Et)
The amount received after compounding at the end of 1 year will be:
![\rm A = 300(1 + \dfrac{5.5}{100})^1\\ \\ A=300(1.055)\\ \\ A=\$316.5](https://tex.z-dn.net/?f=%20%5Crm%20A%20%3D%20300%281%20%2B%20%5Cdfrac%7B5.5%7D%7B100%7D%29%5E1%5C%5C%0A%5C%5C%0AA%3D300%281.055%29%5C%5C%0A%5C%5C%0AA%3D%5C%24316.5)
Similarly, the amount to be received after 2 years will be:
![316.5+316.5(1.055)](https://tex.z-dn.net/?f=316.5%2B316.5%281.055%29)
The amount received after 10 years will be:
upto 10 years
Therefore the summation that represents the money in account after 10 years is:
![\begin{aligned}\sum_{10}^{n=1}316.5(1.055)^{n-1} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csum_%7B10%7D%5E%7Bn%3D1%7D316.5%281.055%29%5E%7Bn-1%7D%20%5Cend%7Baligned%7D)
Learn more about compound interest here:
brainly.com/question/25857212